Sumários

15 Setembro 2021, 18:00 • Pierre Hoonhout

4 types of functions

1 - scalar-valued function of a scalar

2 - scalar-valued function of a vector

first derivative: score-function (column)/gradient-function (row)

second derivative: Hessian matrix

3 - vector-valued function of a scalar

4 - vector-valued function of a vector

first derivative: Jacobi matrix

Linear independence of vectors: Ax=0 <=> x=0

Special matrices

Identity matrix

Diagonal matrix

Symmetric matrix

Inverse matrix: Ax=b <=> x = A^{-1}b if A has an inverse (square with independent columns / det(A) /= 0).

13 Setembro 2021, 21:30 • Pierre Hoonhout

matrix multiplication (two ways of thinking about it)

A'y can be written as a sum (this is simply the second way of thinking about matrix multiplication)

A'B can be written as a sum of outer-products of the rows of A and the rows of B

AB' can be written as a sum of outer-products of the columns of A and the columns of B