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.

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.

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.

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.

See also