My favorites are Matrix Computations by Golub and Van Loan and Numerical Linear Algebra by Trefethen and Bau. Together they cover all the important aspects of the field.

The coordinates of points on the ROC curve are true positive rate (TPR) and false positive rate (TPR). These are given by: $$TPR=TP/(TP+FN)$$ and $$FPR=TP/(TP+FP)$$ The F1 score is given by: $$F_1=2*... View answer 2 votes The simplest example of an optimization problem which can be solved by casting it as a linear equation system is the linear least squares problem$$min_x||Ax-b||_2^2 By deriving this expression, we ...

Since both variables are Gaussian, the natural model for their joint distribution is a multivariate Gaussian distribution.

I suggest that you'd start with learning some basic concepts in probability theory: continuous and discrete random variables, probability density functions, mean, variance and estimating them from a ...

The trivial solution to this problem, which involves brute-forcing the sum of every possible submatrix is O(n^6), which consists of O(n^4) for iterating over all possible submatrices and another O(n^2)...

One way to deal with this problem is to approximate the solution by iterative methods. For example, by using Newton's method to solve the matrix equation $X^2-Y=0$. It leads to the following iteration:...

It's called a Givens rotation. Similarly to Gaussian elimination, you can use a Givens rotation to eliminate a variable from a system of linear equations. The basic idea is to find a 2D rotation ...