Linear Algebra

Matrix Rank

np.linalg.matrix_rank(matrix)

The rank of A matrix is the dimension of the vector space generated by its columns. Maximal number of linearly independent columns of A.

Vector Space

Also called linear space is a set whose elements, often called vectors, can be added together and mutiplied (scaled) by numbers called scalars.

Full Rank

If its rank equals the largest possible for a matrix of the same dimension.

eigendecomposition

The factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors.

factorization

use a product of several factors to represent a variable.

Eigenvalues and eigenvectors

1 sign flips, scaling, repeated eigenvalues are all valid eigenvalues set. Result decided by the inner algorithm. Break thing apart is a good way to understand sth. - It can reduce the computation to O(log n)