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