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March 12, 2020 11:04
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{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# 0.1 공간이라 생각하면 직관이 먹힌다.\n", | |
"- 벡터 공간은 현실 공간의 성질을 특정 수준에서 추상화.\n", | |
"\n", | |
"\n", | |
"- 예) 2차원 물체 -> 3차원 물체\n", | |
"\n", | |
"\n", | |
"- 즉, 단일 수치가 아닌 다수의 수치를 조합한 데이터를 다루고 싶다. (고차원) : Neural Network\n", | |
"\n", | |
"\n", | |
"- 벡터를 고차원 공간 내의 점이라고 생각한다면 직관적인 생각이 가능하다.\n", | |
"\n", | |
"\n", | |
"# 0.2 선형대수가 다루는 대상 : 선형, 즉 곧은 것.\n", | |
"- 다루기 쉬움, 예측하기 좋다, 명쾌한 결과.\n", | |
"\n", | |
"\n", | |
"- 그렇다면 곡선 또는 고차원의 그래프는 어떻게 다룰것인가?\n", | |
" - 어떤 곡선이건간에 zoom up 하면 모두 선형으로 근사할 수 있다." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"from IPython.display import Image" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 4, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": "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\n", | |
"text/plain": [ | |
"<IPython.core.display.Image object>" | |
] | |
}, | |
"execution_count": 4, | |
"metadata": { | |
"image/png": { | |
"width": 200 | |
} | |
}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"Image('./image/linear01.png',width=200)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 5, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": "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\n", | |
"text/plain": [ | |
"<IPython.core.display.Image object>" | |
] | |
}, | |
"execution_count": 5, | |
"metadata": { | |
"image/png": { | |
"width": 200 | |
} | |
}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"Image('./image/linear02.png',width=200)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# 1.1 벡터와 공간\n", | |
"- 많은 수치를 묶은 데이터를 다루고 싶다.\n", | |
" - **수치의 조합**이 아닌 **공간 안의 점**으로 간주.\n", | |
" - **문자 배열**이 아닌 **공간**\n", | |
"\n", | |
"\n", | |
"vector : 숫자를 일렬(1차원) : 화살표, 공간 내 점\n", | |
"matrix : 숫자를 사각형으로 나열(1-고차원) : 공간 -> 공간으로의 사상\n", | |
"행렬식 : 복잡한 계산 : 사상에 따른 부피 확대율\n", | |
"\n", | |
"## 벡터\n", | |
"여러 개의 수치를 한 곳에 모아 덩어리로 다루고 싶다.\n", | |
"수를 나열한 것.\n", | |
"\n", | |
"$(1, 2, 3)^T$ => 벡터는 기본적으로 열벡터.\n", | |
"\n", | |
"### 왜 열 벡터?\n", | |
"함수 : f(x) 즉, Ax 형태로 표기가 가능하다.\n", | |
"\n", | |
"### 연산\n", | |
"$ { x_1 \\choose x_2} + {y_1 \\choose y_2} = {x_1 \\ + \\ y_1 \\choose x_2 \\ + \\ y_2}$ \n", | |
"\n", | |
"$ c{ x \\choose y } = {cx \\choose cy}$\n", | |
"\n", | |
"### 벡터의 성질\n", | |
"1. $ (cc')x = c(c'x)$\n", | |
"2. $ 1x = x$\n", | |
"3. $ x + y = y + x $\n", | |
"4. $ (x + y) + z = x + (y + z)$\n", | |
"5. $ x + 0 = x$\n", | |
"6. $ x + (-x) = 0$\n", | |
"7. $c(x+y) = cx + cy$\n", | |
"8. $(c +c')x = cx + cx'$" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## 1.1.2 '공간'의 이미지\n", | |
"위치 벡터 : 위치에 대응시키는 것을 강조.\n", | |
": 도형으로 해석할 때는 '화살표'가 더 어울린다.(기하학적)\n", | |
"\n", | |
"## 1.1.3 기저\n", | |
"2차원 : 평면 위에 점\n", | |
"3차원 : 공간 위에 점\n", | |
"\n", | |
"'정수배'와 '덧셈'이 정의된 세계를 **선형 공간**이라 한다. \n", | |
"\n", | |
"선형공간에 '길이', '각도'는 정의되어 있지 않다.\n", | |
"- 즉, 대소비교와 각도 회전 개념이 없다.\n", | |
"- 내적 공간이라는 선형 공간의 확장판에서 정의됨.\n", | |
"\n", | |
"\n", | |
"### 기준을 정하여 번지를 매기자.\n", | |
"특정 벡터 $\\vec{v}$를 지정하는데 표현 방법이 없다. \n", | |
"\n", | |
"- 기준이 되는 벡터 $\\vec{e_1}, \\ \\vec{e_2}$를 정한다. : 기저\n", | |
"\n", | |
"\n", | |
"- 예) $\\vec{e_1}$ 3보, $\\vec{e_2}$ 4보처럼 말로 표현이 가능.(좌표)\n", | |
"\n", | |
"\n", | |
"기저를 취하는 방법에 의존하지 않는 실체 : 정칙, 랭크, 고윳값.\n", | |
"\n", | |
"## 1.1.4 기저의 조건\n", | |
"1. 어떤 벡터 $\\vec{v}$라도$\\vec{v} = x_1\\vec{e_1}+x_2\\vec{e_2}+\\dots+x_n\\vec{e_n}$ 형태로 표현이 가능하다.\n", | |
" - 모든 토지에 번지가 붙어 있다.\n", | |
"\n", | |
"\n", | |
"2. 표현 방법은 오직 하나.\n", | |
" - 토지 하나에 번지 하나\n", | |
" \n", | |
"**차원 만큼의 기저가 필요. (모두가 다른 축 방향을 가져야한다.)**\n", | |
"\n", | |
"## 1.1.5 좌표에서 표현\n", | |
"좌표에 기저는 필수.\n", | |
"- 예) 1500 -> ?, 1500m => 아하! (여기서 단위가 기저가 된다.)\n", | |
"\n", | |
"**덧셈과 정수배는 기저에 독립적**\n", | |
"\n", | |
"$\\vec{x} + \\vec{y} = (x_1+y_1)\\vec{e_1}+(x_2+y_2)\\vec{e_2}+\\dots+(x_n+y_n)\\vec{e_n}$ \n", | |
"\n", | |
"$ c\\vec{x} = (cx_1)\\vec{e_1} + (cx_2)\\vec{e_2}+\\dots+(cx_n)\\vec{e_n}$\n", | |
"\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# 1.2 행렬과 사상\n", | |
"대상 간의 **관계**를 나타내기 위해 '행렬'을 사용.\n", | |
"\n", | |
"## 1.2.1 우선적 정의 : 순수 관계를 나타내는 편리한 기법.\n", | |
"행렬 : 수를 사각형 형태로 나열한 것. \n", | |
"\n", | |
"정방행렬 : 행 = 열 \n", | |
"\n", | |
"i행 j열 : A의 (i, j) \n", | |
"\n", | |
"행렬도 정수배와 덧셈이 성립.\n", | |
"\n", | |
"### 곱에 대한 성질\n", | |
"1. 행렬 x 벡터 = 벡터\n", | |
"\n", | |
"\n", | |
"2. 행렬의 열 수 = 입력 차원 수, 행렬의 행 수 = 출력 차원 수\n", | |
"\n", | |
"\n", | |
"## 1.2.2 여러 가지 관계를 행렬로 나타내다 (1)\n", | |
"행렬을 곱하다 = 순수한 관계\n", | |
"- 예) 단순히 각 요인의 합계, 상승 효과나 규모 효과가 없다.\n", | |
"- 상수곱과 덧셈으로만 형성이 되면 순수하다 한다.\n", | |
"\n", | |
"### 순수한 예\n", | |
"$ y_{머리} = a_{학머리}x_{학} + a_{거북머리}x_{거북} = x_{학} + x_{거북}$ \n", | |
"\n", | |
"$ y_{다리} = a_{학다리}x_{학} + a_{거북다리}x_{거북} = 2x_{학} + 4x_{거북}$\n", | |
"\n", | |
"### 순수하지 않은 예\n", | |
"한 개에서 나오는 원료의 양은 20g인데, 1000개에서 나오는 원료의 양은 18000g. \n", | |
"\n", | |
"## 1.2.3 행렬은 사상이다.\n", | |
"n차원 vector x, m x n 행렬 A. \n", | |
": Ax = y. \n", | |
"\n", | |
"**즉, A는 벡터 x를 다른 벡터 y로 옮기는 사상이다**" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"### 사상의 성질\n", | |
"- 원점 O => 원점 O\n", | |
"\n", | |
"\n", | |
"- 직선 -> 직선 또는 찌그러져서 점이 될 수 있다.\n", | |
"\n", | |
"\n", | |
"- 평행선은 평행선으로. (입력이 평행이면 출력도 평행)\n", | |
"\n", | |
"\n", | |
"$e_1 = {1 \\choose 0}$을 ${1 \\choose -0.7}$, $e_2 = {0 \\choose 1}$을 ${ -0.3 \\choose 0.6}$으로 이동. \n", | |
"\n", | |
"=> 행렬 A $\\begin{pmatrix} 1 & -0.3 \\\\ -0.7 & 0.6 \\end{pmatrix}$ 사상." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"- m x n 행렬 A : n차원 vector -> m차원 vector\n", | |
"\n", | |
"\n", | |
"- 사상이 같으면 행렬도 같다.\n", | |
" - Ax = Bx 이면 A=B\n", | |
" \n", | |
"## 1.2.4 행렬의 곱 = 사상의 합성\n", | |
"(k, m) 행렬 x (m, n)행렬 = (k, n) 행렬.\n", | |
"\n", | |
"**즉 벡터 x를 A로 사상시킨 후, B로 한번 더 사상**\n", | |
"\n", | |
"z = B(Ax), like g(f(x))\n", | |
"\n", | |
"### 성질\n", | |
"- $ABC = (AB)C = A(BC)$\n", | |
"\n", | |
"\n", | |
"- $AB \\neq BA$\n", | |
"\n", | |
"### 예\n", | |
"A = $\\begin{pmatrix} 0 & -1 \\\\ 1 & 0 \\end{pmatrix}$ 공간 회전.\n", | |
"B = $\\begin{pmatrix} 2 & 0 \\\\ 0 & 1 \\end{pmatrix}$ 가로로 넓히는, 즉 x축 방향을 늘리는.\n", | |
"\n", | |
"ABx : x벡터를 가로로 넓힌 후, 공간 회전.\n", | |
"BAx : x벡터를 공간 회전 후, 가로로 넓힘.\n", | |
"\n", | |
"## 1.2.5 행렬 연산의 성질\n", | |
"- (cA)x = c(Ax) = A(cx)\n", | |
"\n", | |
"\n", | |
"- (A+B)x = Ax + Bx\n", | |
"\n", | |
"\n", | |
"- A+B = B+A\n", | |
"\n", | |
"\n", | |
"- (A+B)+C = A+(B+C)\n", | |
"\n", | |
"\n", | |
"- (c+c')A = cA + c'A\n", | |
"\n", | |
"\n", | |
"- (cc')A = c(c'A)\n", | |
"\n", | |
"\n", | |
"- A(B+C) = AB+ AC\n", | |
"\n", | |
"\n", | |
"- (A+B)C = AC + BC\n", | |
"\n", | |
"\n", | |
"- (cA)B = c(AB) = A(cB)\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"### 벡터도 행렬?\n", | |
"n차원 vector는 1xn행렬이라 할 수 있다.\n", | |
"행렬의 모든 성질을 만족.\n", | |
"\n", | |
"## 1.2.6 행렬의 거듭 제곱 = 행렬의 반복.\n", | |
"**단, 정방행렬에서만 가능**\n", | |
"\n", | |
"$A\\dots A = A^n$ : A를 n번 반복한다.\n", | |
"\n", | |
"- $(A+B)^2 = A^2 + AB + BA + B^2$\n", | |
"\n", | |
"\n", | |
"- $(A+B)(A-B) = A^2 -AB +BA - B^2$\n", | |
"\n", | |
"\n", | |
"- $(AB)^2 = ABAB$" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## 1.2.7 특수 행렬\n", | |
"### 영행렬 : 모든 성분이 0\n", | |
"\n", | |
"사상: 모든 점을 원점으로 이동시킨다.\n", | |
"\n", | |
"$ A \\neq 0, B \\neq 0$ 이어도 $AB = 0$이 될 수 있다.\n", | |
"\n", | |
"\n", | |
"$ A \\neq 0$ 이어도 $A^2 = 0$이 될 수 있다.\n", | |
"\n", | |
"### 단위행렬 : 대각성분이 1, 나머지는 0\n", | |
"\n", | |
"사상 : 아무것도 하지 않는 사상.\n", | |
"\n", | |
"### 대각행렬 : 비대각 성분이 모두 0\n", | |
"정방행렬에서 대각 부분을 '대각 성분', 나머지 부분을 '비대각 성분' 이라 한다.\n", | |
"\n", | |
"$diag(a_0, a_1, a_2, \\dots a_n)$\n", | |
"\n", | |
"사상 : 축에 따르는 신축(늘고 줄음) 사상.\n", | |
"- 각 성분 값이 배율이 된다.\n", | |
"\n", | |
"예) A= $\\begin{pmatrix} 1.5 & 0 \\\\ 0 & 0.5 \\end{pmatrix}$ \n", | |
"x축 : 1.5배, y축 : 0.5배\n", | |
"\n", | |
"**즉, 각 x원소 개별만이 출력에 영향을 준다.**\n", | |
"\n", | |
"- 대각 행렬끼리의 곱셈\n", | |
"$\\begin{pmatrix} a & 0 \\\\ 0 & b \\end{pmatrix}$ $\\begin{pmatrix} x & 0 \\\\ 0 & y \\end{pmatrix}$ = $\\begin{pmatrix} ax & 0 \\\\ 0 & by \\end{pmatrix}$" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## 1.2.8 역행렬 = 역사상\n", | |
"A로 이동시킨 것을 원래대로 돌리는 사상.\n", | |
"\n", | |
"$Ax = y, x = A^{-1}y$\n", | |
"\n", | |
"역행렬은 존재하거나 안 할수 있다.\n", | |
"\n", | |
"존재하지 않는 경우\n", | |
"- 납작하게 눌리는 경우.\n", | |
" - 서로 다른 두 점(x, x')이 같은 점 y로 이동.\n", | |
" \n", | |
"### 역행렬의 성질.\n", | |
"- $(A^{-1})^{-1} = A$\n", | |
"- $(AB)^{-1} = B^{-1}A^{-1}$\n", | |
"- $ (A^k)^{-1} = (A^{-1})^k$\n", | |
"\n", | |
"\n", | |
"### 대각행렬의 경우\n", | |
"**축에 따른 신축을 되돌리려면?**\n", | |
"\n", | |
"$ A = diag \\left( a_1, a_2,\\dots a_n) => A^{-1} = diag(\\frac{1}{a_1}, \\frac{1}{a_2}, \\dots,\\frac{1}{a_n}\\right)$\n", | |
"\n", | |
"**$a_1, a_2, \\dots a_n$ 중에 하나라도 0이 있다면 역행렬이 존재하지 않는다.**\n", | |
"- 한 차원이 0이 되어 버리므로. 눌리는 현상.\n", | |
"\n", | |
"## 1.2.9 블록행렬\n", | |
"큰 문제를 작은 문제로 분할하고 싶다. \n", | |
"\n", | |
"블록행렬 : 행렬의 종횡에 단락을 넣어 각 구역을 작은 행렬로 간주한 것.\n", | |
"\n", | |
"덧셈과 정수배, 행렬 곱 모두 만족. 단, 서로의 비율이 같아야한다." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 9, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
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| |
"text/plain": [ | |
"<IPython.core.display.Image object>" | |
] | |
}, | |
"execution_count": 9, | |
"metadata": { | |
"image/png": { | |
"height": 400, | |
"width": 400 | |
} | |
}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"Image('./image/linear03.png', width=400, height=400)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## 1.2.10 여러가지 관계를 행렬로 나타내다(2)\n", | |
"\n", | |
"약간의 트릭을 이용하여 식을 행렬과 벡터 곱으로 쉽게 나타낼 수 있다.\n", | |
"\n", | |
"### 고계차분 , 고계미분\n", | |
"\n", | |
"$$ x_t = -0.7x_{t-1} -0.5x_{t_2}+0.2 x_{t-3} + 0.1 x_{t-4}$$\n", | |
": 최초의 상태로부터 다음 번 상태가 결정된다.\n", | |
"\n", | |
"$$ x(t) = \\begin{pmatrix} x_{t} \\\\ x_{t-1} \\\\ x_{t-2} \\\\ x_{t-3} \\end{pmatrix} = \\begin{pmatrix} -0.7 & -0.5 & 0.2 & 0.1 \\\\ 1 & 0 & 0 & 0 \\\\ 0 & 1 & 0 & 0 \\\\ 0 & 0 & 1 & 0 \\end{pmatrix} \\begin{pmatrix} x_{t-1} \\\\ x_{t-2} \\\\ x_{t-3} \\\\ x_{t-4} \\end{pmatrix}$$" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## 1.2.11 좌표 변환과 행렬\n", | |
"- 같은 공간에서도 기저를 취하는 방법은 여러가지.\n", | |
"- 문제에 따라 적절한 기저를 취해야한다.\n", | |
"\n", | |
"좌표 변환 : '정방행렬 A'를 곱한다.\n", | |
"\n", | |
"$\\vec{v} = x\\vec{e_x} + y\\vec{e_y} = x'\\vec{e'_x}+y'\\vec{e'_y}$\n", | |
"\n", | |
"좌표 v와 v'의 대응관계는 어떻게 될까?\n", | |
"\n", | |
"$e_x를 e'_x, e'_x를 e_x$식으로 표현이 가능하다.\n", | |
"즉, 기저가 바뀌면 그 앞 계수는 달라지지만 실제 값은 동일하다.\n", | |
"\n", | |
"예) 1780m = 1.78km. 단위가 바뀌어 계수가 달라졌지만 값은 동일.\n", | |
"\n", | |
"## 1.2.12 전치행렬=?\n", | |
"$A^T$\n", | |
"\n", | |
"사상 : 단순 선형 공간에서는 정의되지 않는다.\n", | |
"\n", | |
"### 성질\n", | |
"- $(A^T)^T = A$ \n", | |
"- $(AB)^T = B^TA^T$ \n", | |
"- $diag(A)^T = diag(A)$\n", | |
"- $(A^{-1})^T = (A^T)^{-1}$\n", | |
"\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## 1.3\n", | |
"행렬식과 확대율.\n", | |
"\n", | |
"## 1.3.1 행렬식 = 부피 확대율\n", | |
"\n", | |
"A = $\\begin{pmatrix} 1.5 & 0 \\\\ 0 & 0.5 \\end{pmatrix}$ \n", | |
"가로 1.5배, 세로 0.5 배 => 면적 = 1.5 x 0.5\n", | |
"\n", | |
"**면적 확대율**에 관한 것을 그 행렬의 **행렬식**이라한다.\n", | |
"- 3차원일 경우, 부피 확대율.\n", | |
"\n", | |
"$det A = |A|$\n", | |
"\n", | |
"도형이 납작하게 되는 경우는 확대율이 0.\n", | |
"\n", | |
"정방행렬에서만 정의된다.\n", | |
"\n", | |
"## 1.3.2 행렬식의 성질\n", | |
"- det I = 1\n", | |
"- det(AB) = (detA)(detB)\n", | |
"- $detA^{-1} = \\frac{1}{detA}$\n", | |
"- detA=0이면 역행렬이 존재하지 않는다.\n", | |
"- $det(diag(a_1,\\dots, a_n)) = a_1*a_2*\\dots*a_n$\n", | |
"\n", | |
"### 유용한 성질\n", | |
"\n", | |
"행렬식은 **어느 열의 정수배를 다른 열에 더해도 값이 변하지 않는다.**\n", | |
"\n", | |
"즉, det$\\begin{pmatrix} 1 & 1 & 5 \\\\ 1 & 2 & 7 \\\\ 1 & 3 & 6 \\end{pmatrix} = \\begin{pmatrix} 1 & 1 & 5+1*10 \\\\ 1 & 2 & 7+2*10 \\\\ 1 & 3 & 6+3*10 \\end{pmatrix}$ \n", | |
"\n", | |
"2열을 10배한 값을 3열에 더해준것.\n", | |
"\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"### upper triangular\n", | |
"\n", | |
"$\\begin{pmatrix} a_{11} & a_{12} & a_{13} \\\\ 0 & a_{22} & a_{23} \\\\ 0 & 0 & a_{33} \\end{pmatrix}$\n", | |
"\n", | |
"우상삼각 x 우상삼각 = 우상삼각 \n", | |
"좌하삼각 x 좌하삼각 = 좌하삼각\n", | |
"\n", | |
"### 전치행렬의 행렬식\n", | |
"$det(A^T) = det(A)$ \n", | |
"행렬식의 성질은 행과 열의 역할을 모두 바꾸어도 성립.\n", | |
"\n", | |
"### 열쇠가 되는 성질.\n", | |
"$det(ca_1, a_2,\\dots a_n) = cdet(a_1,a_2,\\dots,a_n)$\n", | |
"- det(cA) - $c^n$det(A) \n", | |
"$det(a_1+a'_1, a_2, \\dots, a_n) = det(a_1, a_2,\\dots,a_n) + det(a'_1,a_2,\\dots,a_n)$\n", | |
"\n", | |
"행렬식의 부호가 도형의 뒤집음과 대응하고 있으므로 => **두 열을 바꾸면 부호가 역전**\n", | |
"\n", | |
"$det(a_2, a_1, \\dots, a_n) = -det(a_1, a_2, \\dots, a_n)$" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# 2.1 문제 설정:역문제\n", | |
"**결과를 알고 있고, 원인을 추측하고 싶다**\n", | |
"\n", | |
"# 2.2 성질이 좋은 경우(정칙행렬)\n", | |
"## 2.2.1 정칙성과 역행렬\n", | |
"행과 열이 같은 행렬을 **정방행렬**이라 한다.\n", | |
"\n", | |
"역행렬 : $x=A^{-1}y$\n", | |
"\n", | |
"역행렬이 존재하는 정방행렬을 **정칙행렬**라 한다.\n", | |
"\n", | |
"## 2.2.2 가우스 요르단 소거법" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 4, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
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\n", | |
"text/plain": [ | |
"<IPython.core.display.Image object>" | |
] | |
}, | |
"execution_count": 4, | |
"metadata": { | |
"image/png": { | |
"width": 500 | |
} | |
}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"Image('./image/linear04.png',width=500)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## 2.2.3 역행렬의 계산\n", | |
"(A | I) => (I | X)\n", | |
"\n", | |
"즉, identity matrix와 같이 블록으로 만들은 후, A->I가 되게 변환하면 오른쪽 블럭에 나오는 행렬이 $A^{-1}$이 된다.\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# 2.3 성질이 나쁜 경우\n", | |
"## 2.3.1 성질이 나쁜 예\n", | |
"### 단서가 부족한 경우(가로가 긴 행렬)\n", | |
"원인 $ x=(x_1,\\dots,x_n)$과 결과 $y=(y_1,\\dots,y_n)$의 차원 수가 다른 경우는 어떨까?\n", | |
"먼저 y가 x보다 차원이 작은 경우를 생각해 보자.\n", | |
"\n", | |
"$\\begin{pmatrix} c \\\\ d \\end{pmatrix} = \\begin{pmatrix} a & b & k \\\\ i & j & h\\end{pmatrix} \\begin{pmatrix} x \\\\ y \\\\ z \\end{pmatrix}$\n", | |
"\n", | |
"\n", | |
"\n", | |
"\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"여기서 행렬 A는 x가 사는 3차원 공간을 y가 사는 2차원 공간으로 매핑하는 사상이 된다.\n", | |
"- 원래 차원보다 저차원으로 사상되므로 **'납작하게 눌리는 사상'**이 된다.\n", | |
"- 즉, 여러 개의 x가 같은 y로 이동하는 꼴이 된다.\n", | |
"- 해가 여러개." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 9, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<IPython.core.display.Image object>" | |
] | |
}, | |
"execution_count": 9, | |
"metadata": { | |
"image/png": { | |
"width": 300 | |
} | |
}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"Image('./image/linear05.png',width=300)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"여기서 **Ker A**라는 것은, 사상 했을 시에 원점으로 매핑되는 영역을 말한다.\n", | |
"- 사상 A에서 납작하게 눌려지는 방향.\n", | |
"\n", | |
"### 단서가 너무 많은 경우(세로가 긴 행렬)\n", | |
"x보다 y의 차원이 큰 경우.\n", | |
"**'단서끼리 서로의 모순이 있는 경우'**\n", | |
"\n", | |
"$\\begin{pmatrix} c \\\\ d \\\\ f\\end{pmatrix} = \\begin{pmatrix} a & b \\\\ i & j\\\\ m & n\\end{pmatrix} \\begin{pmatrix} x \\\\ y \\end{pmatrix}$\n" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 8, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<IPython.core.display.Image object>" | |
] | |
}, | |
"execution_count": 8, | |
"metadata": { | |
"image/png": { | |
"width": 300 | |
} | |
}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"Image('./image/linear06.png',width=300)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"원래보다 높은 차원으로 이동.\n", | |
"- 고차원의 모든 공간을 커버하는 것이 불가능하다.\n", | |
"- 어떤 y에 대해서는 대응되는 x가 존재하지 않는다.\n", | |
" - 현실에서 노이즈에 의해 발생할 수 있다. 즉, 있어야하면 안되는 y가 관찰 될 수 있음.\n", | |
" \n", | |
"여기서 **ImA**는 x가 주어진 A에 의해 사상되어 옮겨진 모든 y의 집합.\n", | |
"- 원래 공간 전체를 A로 매핑시킨 영역.\n", | |
"\n", | |
"### 단서의 개수가 일치하면 다 맞는것일까?\n", | |
"**성질의 좋고 나쁨은 행렬의 형태가 아닌, 'KerA나 ImA가 어떻게 되어 있는가'에 따른다.**\n", | |
"\n", | |
"## 2.3.2 성질의 나쁨과, 핵과 상\n", | |
"\n", | |
"### 조건\n", | |
"1. 하나의 결과 y에서 나오는 원인 x는 유일한가.\n", | |
"2. 모든 y에 대해 그것이 나오는 원인, x가 존재하는가." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"조건 1을 만족하면 **단사**. \n", | |
"조건 2를 만족하면 **전사**. \n", | |
"조건 1, 2를 모두 만족하면 **전단사**라 한다.\n", | |
"\n", | |
"- KerA가 원점 O뿐이라면 단사. \n", | |
"- ImA가 목적지의 전 공간과 일치하면 전사.\n", | |
"\n", | |
"## 2.3.3 차원 정리\n", | |
"mxn 행렬에 대해 **dim KerA + dim ImA = n**이다.\n", | |
"- A는 n차원 공간을 m차원 공간으로 매핑시키는 사상이다.\n", | |
"- 원래의 n차원 공간에서 KerA의 차원 부분이 눌리고 남은 것이 ImA의 차원 부분.\n", | |
"\n", | |
"또한, m < n(가로가 긴, 눌리는 사상) 행렬에 대해서는 단사가 될 수 없고.\n", | |
"m > n(세로가 긴, 단서가 많은 사상) 행렬에 대해서는 전사가 될 수 없다.\n", | |
"\n", | |
"## 2.3.4 '납작하게'를 식으로 나타내다. (선형종속, 독립)\n", | |
"**'납작하게 눌린다'**는 '서로 다른 x와 x'이 같은 y로 매핑된다'를 의미한다.\n", | |
"\n", | |
"즉, $Ax = Ax', \\ \\ a_1x_1+a_2x_2+\\dots+a_nx_n = a_1x'_1+a_2x'_2+\\dots+a_nx'_n$ 이라 하고, \n", | |
"이 조건이 성립되는 A는 **선형 종속**이라 한다. 성립되지 않는 경우를 **선형 독립**. \n", | |
"\n", | |
"다른 조건으로는, \n", | |
"$x_1v_1+x_2v_1+\\dots+x_nv_n = 0$일 때, $x_1, x_2,\\dots,x_=0$인 해만 존재한다면 **선형 독립**. \n", | |
"아니라면 **선형 종속**이라 한다. \n", | |
"\n", | |
"여기서 하나 알 수 있는 사실은 '기저 벡터는 선형 독립이어야만 한다'이다.\n", | |
"\n", | |
"### 기저 = 선형독립?\n", | |
"기저가 조금 더 조건에서 엄격하다.\n", | |
"- 기저에는 **모든 토지에 번지가 붙는다**라는 조건이 붙는다.\n", | |
"\n", | |
"예) (1,0,0)과 (0,1,0)은 선형독립이지만 기저는 아니다." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## 2.3.5 단서의 실질적인 개수(랭크)\n", | |
"이번에는 '이동점의 공간 전체를 커버할 수 있는가'를 알아보자. \n", | |
"즉 , **Im A가 공간 전체를 커버하고 있는가**이다.\n", | |
"\n", | |
"Im A의 차원을 알게 되면, 그 차원이 '단서의 실질적인 개수'가 되고, '납작하게 눌리는가'도 알 수 있다.\n", | |
"\n", | |
"### 랭크의 정의\n", | |
"m x n 행렬 A가 있다고 하자. \n", | |
"즉, n차원 벡터 x를 A사상시켜 m차원 y로 매핑시키는 것을 말한다. \n", | |
"\n", | |
"여기서 dim Im A를 **행렬 A의 랭크**라고 한다. 기호로는 rank A. \n", | |
"\n", | |
"이전의 차원 정리 식을 rank A로 대체하면 \n", | |
"$ dim Ker A + rank A = n$이라 할 수 있고, 이 차원 정리 덕분에 rank A를 알면 Ker A를 아는 것과 같다.\n", | |
"\n", | |
"### 랭크와 핵, 상과 단사, 전사\n", | |
"우리의 관심은 다음과 같다.\n", | |
"- Ker A가 원점 O뿐인가? = Ker A는 0차원인가?\n", | |
"- Im A가 m차원 공간 전체를 커버하는가? = Im A는 m차원 인가?\n", | |
"\n", | |
"이것을 랭크나 차원 정리를 사용해 다시 말하면,\n", | |
"- rank A=n (랭크가 원래 공간(정의역)의 차원과 동일) <=> A는 단사.\n", | |
"- rank A=m (랭크가 목적지 공간(치역)의 차원과 동일) <=> A는 전사." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"### 랭크의 기본 성질\n", | |
"우선 A가 m x n이라 하자. \n", | |
"먼저, $rank A \\le m$, $rank A \\ge n$이다. \n", | |
"당연히 rank A는 이전 x들이 사상되어 m차원의 공간으로 매핑된 것이기 때문에 m과 n보다 클 수 없다.\n", | |
"\n", | |
"또한, **정칙행렬을 곱해도 랭크는 변하지 않는다.** \n", | |
"- rank(PA) = rank(A)\n", | |
"- 정칙행렬은 납작하게 눌리는 경우가 아니기 때문에, rank에 영향을 주지 않는다.\n", | |
"\n", | |
"일반행렬에 대해서는, \n", | |
"- $rank(BA) \\le rank A$\n", | |
"- 만약 B가 눌리는 사상이라면 rank가 작아지기 때문이다.\n", | |
"\n", | |
"마지막으로 전치해도 랭크는 동일하다.\n", | |
"- $rank A^T = rank A$\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# 2.4 성질의 좋고 나쁨의 판정(역행렬이 존재하기 위한 조건)\n", | |
"A가 정방행렬이 아닌 경우, 해의 존재성이나 일의성 어느 한쪽에 문제가 발생한다. \n", | |
"따라서 여기서는 A가 정방행렬인 경우로 한정한다. \n", | |
"\n", | |
"## 2.4.1 '납작하게 눌리는가'가 포인트\n", | |
"정방행렬에서는 특히 **납작하게 눌리는가**가가 포인트이다.\n", | |
"\n", | |
"납작하게 눌리지 않는다 => Ker A가 원점 O뿐이다. => rank A = n.\n", | |
"\n", | |
"납자갛게 눌린다면 역행렬이 없다!!\n", | |
"\n", | |
"## 2.4.2 정칙성과 같은 조건 여러 가지.\n", | |
"- A의 사상은 납작하게 눌리지 않는다.\n", | |
"- A의 사상은 단사.\n", | |
"- Ker A가 원점 O뿐.\n", | |
"- dim Ker A = 0\n", | |
"\n", | |
"\n", | |
"- A의 사상은 '목적지 공간 전체를 커버한다.'\n", | |
"- A의 사상은 전사.\n", | |
"- Im A가 n차원 공간 전체.\n", | |
"- rank A = dim Im A = n\n", | |
"\n", | |
"\n", | |
"- $A = (a_1, a_2, \\dots, a_n)$은 선형독립.\n", | |
"- Ax = 0이 되는 해는 x=0뿐.\n", | |
"\n", | |
"\n", | |
"- $det A \\neq 0$\n", | |
"\n", | |
"\n", | |
"- A가 고윳값 0을 지니지 않는다.\n", | |
"\n", | |
"\n", | |
"- $rank A = n과 \\ rank A^T = n $이 동치라는 것은 'A가 정칙'\n", | |
" - n은 전치되었을 때의 n인 듯하다." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## 2.4.3 정칙성의 정리\n", | |
"1. 어떤 n차원 벡터 y에도 y = Ax가 되는 x가 딱 한 개 있다.\n", | |
"2. A는 정칙행렬(역행렬이 존재)\n", | |
"3. A의 사상은 '납작하게 눌리지 않는다.'\n", | |
"4. Ax = 0이 되는 것은 x=0뿐.\n", | |
"5. A의 열벡터 $a_1, a_2, \\dots, a_n$이 선형독립.\n", | |
"6. A의 사상은 '목적지 공간 전체를 커버한다'\n", | |
"7. rank A = dim Im A = n\n", | |
"8. det A $\\neq$ 0\n", | |
"9. A가 고윳값 0을 지니지 않는다.\n", | |
"10. 이상의 A를 $A^T$로 치환한 것.\n", | |
" - rank A = rank $A^T$를 말하는 듯." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# 2.5 성질이 나쁜 경우의 대책\n", | |
"## 2.5.1 구할 수 있는데까지 구한다.\n", | |
"성질이 나쁜 행렬 A에서는 **해 x가 존재하지 않거나**, **해 x가 무수히 많이 존재한다**가 된다.\n", | |
"\n", | |
"\n", | |
"- 어떠한 해를 x라 하면, ker A에 속하는 z에 대해, x + z도 해가 된다. \n", | |
"- Ker A란 무엇인가에서 알 수 있다.\n", | |
"- $ A(x+ z) = Ax + Az= y + 0 = y $\n", | |
"\n", | |
"## 2.5.2 최소제곱법\n", | |
"x의 방정식 Ax = y에 대해 '해가 없다면 없다고 답한다. 해가 무수히 많다면 모두를 답한다.'가 이전의 이야기였다.\n", | |
"\n", | |
"그러나 현실에서는 단 하나의 해를 원하는 경우가 많다.\n", | |
"\n", | |
"이 경우에는 다음과 같은 방식을 사용한다.\n", | |
"- 해가 없다면 적어도 Ax가 y에 **최대한 가까운 것 같은**x를 구한다.\n", | |
"- 해x가 많다면 그 중에서 **가장 그럴듯한**것을 고른다.\n", | |
"\n", | |
"이러한 방식을 사용할 때, 자주 사용하는 기준이 최소제곱법이다.\n", | |
"- Ax - y 의 길이가 작으면 가까운.\n", | |
"- x의 길이가 작으면 그럴 듯한." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": {}, | |
"outputs": [], | |
"source": [] | |
} | |
], | |
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"kernelspec": { | |
"display_name": "Python 3", | |
"language": "python", | |
"name": "python3" | |
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"name": "ipython", | |
"version": 3 | |
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"file_extension": ".py", | |
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"name": "python", | |
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"version": "3.7.4" | |
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