linear algebra (matrix algebra)

linear-algebra-cheatsheet.org

matrix multiplication

https://youtu.be/XkY2DOUCWMU?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab q stores matrices in column-major order - it means that first element of each list is first column, second element is second column etc

special case: float vector is Nx1 or 1xN (if enlisted) matrix

q)enlist[1 2 3f] $ 1 2 3f                            / rows times columns
,14f
q)(1 3f;-2 0f)$-1 2f                                 / 5 2; (x-axis coords;y-axis coords); has columns 1 -2 and 3 0
q)(1 1f;0 1f)$(0 -1f;1 0f)                           / (1 -1f;1 0f);

q)(1 2 3f;4 5 6f)$(7 8f;9 10f;11 12f)                / 58 64  139 154; rows dot columns
q)(1 2 3f;4 5 6f)$\:(7 8f;9 10f;11 12f)                / 58 64  139 154

q)((enlist each 1 4f)$enlist 7 8f) +
 ((enlist each 2 5f)$enlist 9 10f) +
 (enlist each 3 6f)$enlist 11 12f

eigenvectors and eigenvalues

https://youtu.be/PFDu9oVAE-g?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab eigen vector is the axis of rotation, eigenvalue is scaling/squishing along that axis. all other vectors after rotation end up outside their own span, except eigenvectors

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