Linear Algebra

Using

using DoubleFloats, LinearAlgebra

Vectors and Matrices

using DoubleFloats, LinearAlgebra

n = 25
vector = rand(Double64, n)
matrix = reshape(rand(Double64,n*n),n,n)

Matrix Predicates

• iszero, isone, isdiag
• issquare, issymmetric, ishermitian
• isposdef, isposdef!
• istril, istriu

Matrix Operations

• +, -, *, /
• rank, cond, norm, opnorm
• diagind, diag
• transpose, adjoint
• inv, pinv

Matrix Functions

• det, logdet, logabsdet, tr
• eigvals, eigvals!, eigvecs, eigen
• svdvals, svdvals!, svd

Matrix Factorizations

• general: lu, lu!, qr, qr!
• square: schur, schur!, hessenberg, hessenberg!
• square+symmetric, Hermitian: cholesky, cholesky!

Functions of Matrices (diagonalizable & square only)

• sqrt, cbrt

• matrix^power

• exp, log

• sin, cos, tan, csc, sec, cot

• asin, acos, atan, acsc, asec, acot

• sinh, cosh, tanh, csch, sech, coth

• asinh, acosh, atanh, acsch, asech, acoth

• matrixfunction(function, matrix)