Matrix functions

Matrix construction

MAKE(r,c,[v])Creates a r × c matrix (r rows and c columns) with all elements equal to v.
MAGIC(n) Creates a n × n matrix with as elements the integers 1 through n², with equal row and column sums.
MRND(r,c) Creates a r × c matrix (r rows and c columns) with random numbers.
DIAG(A) Creates a diagonal matrix.
UNIT(A) Returns a unit matrix with the same dimensions of the square matrix A.
ONES(A) returns a matrix with the same dimensions as matrix A with all elements equal to 1.
ZERO(A) Returns a matrix with the same dimensions as matrix A with all elements equal to zero.
CVEC(min,max,n) Returns a column vector with n number or rows, with evenly spaced values ranging from min to max.
RVEC(min,max,n) Returns a row vector with n number or columns, with evenly spaced values ranging from min to max .

Add and remove columns and rows

CBIND(A,B[,..]) Returns a matrix with matrix B appended to matrix A, columnswise.
RBIND(A,B[,..]) Returns a matrix with matrix B appended to matrix A, rowwise.
CDEL(A,c) Returns the matrix A without column c.
RDEL(A,r) Returns the matrix A without row r.
CLEAN(A) Returns a matrix with empty columns and rows with missing data removed.

Matrix properties

INDEX(A,r,c) Returns an element, row, or column of a matrix.
NORM(A) Returns the 2-norm of a vector or matrix.
NCOL(A) Returns the number of columns of a matrix.
NROW(A) Returns the number of rows of a matrix.
TRACE(A) Returns the sum of the elements on the main diagonal of a matrix.

Matrix Operations and Transformations

KRON(A,B) Returns the Kronecker tensor product of matrices A and B.
INV(A) Returns the inverse matrix of a matrix.
PINV(A) Returns the Moore-Penrose Pseudoinverse of a matrix.
RANK(A) Returns an estimate of the number of linearly independent rows or columns of a matrix.
TRANSPOSE(A) Returns the transpose of a matrix.
WINSORIZE(A,k) Returns a matrix with column-wise winsorized values.

Linear Equations

BALANCE(A) Returns a better-balanced matrix with the same eigenvalues.
DETERM(A) Returns the determinant of a matrix.
HESSENBERG(A) Generates a Hessenberg matrix.
EIG(A[,v]) Returns the Eigenvalues of matrix A.
SOLVE(A,B) Solves the equation AX=B for X.
MCOV(A) Returns the variance-covariance matrix.
MCOR(A) Returns the correlation matrix.
SSCP(A) Returns a matrix with sums of squares and cross-products.

Resampling

RESAMPLE(A) Returns a matrix with the same dimension of A, containing a random selection of rows of A (resampling with replacement). Some rows of A may be duplicated in the result matrix, others may be missing.
SUBSAMPLE(A,n) Returns a matrix with n number of rows, selected randomly from the rows of matrix A. Each row of A can only be present once in the result matrix.

Matrix statistical functions

CMAX(A) Returns a row vector with column maxima.
CMIN(A) Returns a row vector with column minima.
CSSQ(A) Returns a row vector with the sum of the squared values of each column.
CSUM(A) Returns a row vector with column totals.
MMAX(A) Returns the numerically maximum value in a matrix.
MMIN(A) Returns the numerically minimum value in a matrix.
MSSQ(A) Returns the sum of the squared values of all of the elements in a matrix.
MSUM(A) Returns the sum of all of the elements in a matrix.
RMAX(A) Returns a column vector with row maxima.
RMIN(A) Returns a column vector with row minima.
RSSQ(A) Returns a column vector with the sum of the squared values of each row.
RSUM(A) Returns a row vector with row totals.

Recommended book

Matrix Algebra Useful for Statistics
Shayle R. Searle, Andre I. Khuri

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This book addresses matrix algebra that is useful in the statistical analysis of data as well as within statistics as a whole. The material is presented in an explanatory style rather than a formal theorem-proof format and is self-contained.