Vector and Matrix Functions

Creating and subdividing arrays

augment, stack, submatrix concatenating and extracting arrays

matrix, diag, identity create various types of arrays from the command line

logpts creates a vector of logarithmically-spaced points

Characteristics of an Array

cols, rows size of a matrix

length, last size of a vector

max, min maximum and minimum values in an array

cond1, cond2, conde, condi condition numbers

norm1, norm2, norme, normi norms

rank, geninv, rref matrix rank, left-inverse, and reduced-row echelon form

eigenvals, eigenvecs, eigenvec, genvals, genvec, tr eigenvalues, eigenvectors, and trace

correl, correl2d 1D and 2D correlation of vectors and matrices.

Decomposition/Factorization

Matrix factorization is frequently a more expedient method to solve linear systems problems, since it's often not optimal to explicitly invert a matrix or calculate a determinant. In applied statistics, matrix factorization can also be used to present structure within data.

cholesky decomposition, a kind of matrix square root

lu LU decomposition into lower and upper triangular matrices

qr QR decomposition into an orthonormal and upper triangular matrix

svds, svd singular values and singular value decomposition