# Package dev.nm.algebra.linear.matrix.doubles.operation

• Class Summary
Class Description
ColumnBindMatrix
A fast "cbind" matrix from vectors.
CongruentMatrix
Given a matrix A and an invertible matrix P, we create the congruent matrix B s.t., B = P'AP
DiagonalSum
Add diagonal elements to a matrix, an efficient implementation.
ElementaryOperation
There are three elementary row operations which are equivalent to left multiplying an elementary matrix.
FastKroneckerProduct
This is a fast and memory-saving implementation of computing the Kronecker product.
InnerProduct
The Frobenius inner product is the component-wise inner product of two matrices as though they are vectors.
Inverse
For a square matrix A, the inverse, A-1, if exists, satisfies A.multiply(A.inverse()) == A.ONE() There are multiple ways to compute the inverse of a matrix.
KroneckerProduct
Given an m-by-n matrix A and a p-by-q matrix B, their Kronecker product C, also called their matrix direct product, is an (mp)-by-(nq) matrix with entries defined by cst = aij bkl where
MAT
MAT is the inverse operator of SVEC.
MatrixFactory
These are the utility functions to create a new matrix/vector from existing ones.
MatrixMeasure
A measure, μ, of a matrix, A, is a map from the Matrix space to the Real line.
MatrixRootByDiagonalization
The square root of a matrix extends the notion of square root from numbers to matrices.
MatrixUtils
These are the utility functions to apply to matrices.
OuterProduct
The outer product of two vectors a and b, is a row vector multiplied on the left by a column vector.
Pow
This is a square matrix A to the power of an integer n, An.
PseudoInverse
The Moore-Penrose pseudo-inverse of an m x n matrix A is A+.
SimilarMatrix
Given a matrix A and an invertible matrix P, we construct the similar matrix B s.t., B = P-1AP
SubMatrixRef
This is a 'reference' to a sub-matrix of a larger matrix without copying it.
SVEC
SVEC converts a symmetric matrix K = {Kij} into a vector of dimension n(n+1)/2.
SymmetricKronecker
Compute the symmetric Kronecker product of two matrices.
VariancebtX
Computes $$b'Xb$$.