Matrix functions

These functions perform matrix operations:

`PRODUCT`	Matrix product (the same as the operator *+)
`LTPRODUCT`	Product after transposing left matrix, i.e. L′ *+ R
`RTPRODUCT`	Product after transposing right matrix, i.e. L *+ R′
`QPRODUCT`	Quadratic product, i.e. M + S + M′
`QTPRODUCT`	Quadratic transposed matrix product, i.e. M′ + S + M
`DETERMINANT`	Determinant of a square matrix
`INVERSE`	Inverse of a square, symmetric or diagonal matrix
`GINVERSE`	Moore-Penrose generalized inverse
`TRANSPOSE`	Transpose of a matrix, i.e. M′
`TRACE`	Trace of a square matrix
`CHOLESKI`	Choleski decomposition of a matrix
`EVALUES`	Eigenvalues (as a diagonal matrix)
`EVECTORS`	Eigenvectors (as a rectangular matrix)
`SVALUES`	Singular values (as a diagonal matrix)
`LSVECTORS`	Matrix of left-hand vectors from a singular-value decomposition
`RSVECTORS`	Matrix of right-hand vectors from a singular-value decomposition
`DPRODUCT`	Direct product of matrices (synonym `KRONECKER`)
`DSUM`	Direct sum of matrices
`MCENTRE`	Doubly centre matrix so that rows and columns have mean zero
`MEXP`	Matrix exponential
`MPOWER`	Matrix power
`MSQRT`	Matrix square root
`CORRMAT`	Correlation matrix derived from a symmetric matrix
`SUBMAT`	Forms sub-triangles or sub-rectangles
`DIAGONAL`	Forms a diagonal matrix from a variate, or takes diagonal (or banded diagonal) of a square, symmetric or diagonal matrix
`LTRIANGLE`	Takes lower triangle of a square matrix (setting upper to zero)
`UTRIANGLE`	Takes upper triangle of a square matrix (setting lower to zero)
`COLBIND`	Joins two matrices side by side
`COLSUMS`	Sums of columns
`COLMEANS`	Means of columns
`COLNOBSERVATIONS`	Numbers of non-missing elements in columns
`COLCENTRE`	Centres columns by subtracting their means
`ROWBIND`	Joins (i.e. stacks) two matrices vertically
`ROWSUMS`	Sums of rows
`ROWMEANS`	Means of rows
`ROWNOBSERVATIONS`	Numbers of non-missing elements in rows
`ROWCENTRE`	Centres rows by subtracting their means
`MINSERT`	Inserts a matrix into another matrix.
`SOLUTION`	Solution of simultaneous linear equations
`VEC`	Stacks columns of a matrix into a single variate
`VECH`	Stacks columns of the lower triangle of a matrix

These functions generate matrices with particular structures:

`IDENTITY`	Identity matrix
`COL1`	Column matrix of 1’s
`ROW1`	Row matrix of 1’s
`MAT1`	Matrix of ones
`BASE`	Column matrix with `n` rows, value one in row `i` and zero elsewhere
`MBASE`	Matrix with ones at specified positions, and zeros elsewhere
`MZERO`	Zero matrix
`MAT0`	Synonym of `MZERO`

These functions give information about matrices:

`NCOLUMNS`	Gives the number of columns of a matrix
`NROWS`	Gives the number of rows of a matrix

These functions form matrices from tables:

`TCOLUMN`	Converts a one-way table into a column matrix
`TDIAGONAL`	Converts a one-way table into a diagonal matrix
`TMATRIX`	Converts a two-way table into a matrix
`TROW`	Converts a one-way table into a row matrix

Updated on May 20, 2019

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