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## HP 39g, 39G+, 40g and 40gs Calculators - Matrix Functions and Commands

Description
Functions
Functions can be used in any APLET or in HOME. They are listed in the MATH menu under the MATRIX CATEGORY. They can be used in mathematical expressions (primarily in HOME) as well as in programs. Functions always produce and display a result. They do not change any stored variables such as a matrix variable.
Functions have arguments that are enclosed in parentheses and separated by commas; for example CROSS(vector1, and vector2). The matrix input can be either a matrix variable name (such as MI) or the actual matrix data inside brackets. For example, CROSS(M1, [1, 2]).
Commands
Matrix commands are listed in the CMDS menu (SHIFT, then CMDS), in the MATRIX CATEGORY. Functions differ from commands in that a function can be used in an expression, whereas commands can not.
Argument conventions
The argument conventions for commands and functions are:
• For row number or column number, supply the number of the row (counting from the top, starting with 1) or the number of the column (counting from the left, starting with one)
• The argument matrix can refer to either a vector or a matrix
Matrix functions
The following table lists the matrix functions for the calculator.
 Function Description COLNORM(matrix) Column norm: finds the maximum value (over all columns) of the sums of the absolute values of all elements in a column COND(matrix) Condition number: finds the 1-norm (column norm) of a square matrix CROSS(vector 1, vector 2) Cross product of vector 1 with vector 2 DET(matrix) Determinant of a square matrix DOT(matrix1, matrix2) Dot product of two arrays, matrix1 matrix2 EIGENVAL(matrix) Displays the eigenvalues in vector form for matrix EIGENVV(matrix) Eigenvectors and Eigenvalues for a square matrix. Displays a list of two arrays. The first contains the eigenvectors and the second contains the eigenvalues IDENMAT(size) Identity matrix: creates a square matrix of dimension (size x size) whose diagonal elements are 1 and off diagonal elements are zero INVERSE(matrix) Inverts a square matrix (real or complex) LQ(matrix) LQ factorization: Factors an m x n matrix into three matrices: {[[m x n lowertrapezoidal]], [[n x n orthogonal]], and [[m x m permutation]]}. LSQ(matrix1, matrix2) Least squares: displays the minimum norm least squares matrix (or vector) LU(matrix) Lu decomposition: factors a square matrix into three matrices: {[[lowertriangular]], [[uppertriangular]], and [[permutation]]}. The uppertriangular has ones on its diagonal. MAKEMAT(expression, rows, columns) Make matrix: creates a matrix of dimension rows x columns, using expressions to calculate each element. If the expression contains the variables I and J, then the calculation for each element substitutes the current row number for I and the current column number for J Example:MAKEMAT(0, 3, 3) returns a 3 x 3 zero matrix, [[0, 0, 0], [0, 0, 0], [0, 0, 0]] QR(matrix) QR factorization: factors an m x n matrix into three matrices: {[[m x m orthogonal]], [[m x n uppertrapezoidal]], [[n x n permutation]]} RANK(matrix) Rank of rectangular matrix ROWNORM(matrix) Row norm: finds the maximum value (over all rows) for the sums of absolute values of all elements in a row RREF(matrix) Reduced row echelon form: changes a rectangular matrix to its reduced row-echelon form SCHUR(matrix) Schur decomposition: Factors a square matrix into two matrices. If the matrix is real then the result is {[[orthogonal]], [[upper-quasi triangular]]}. If the matrix is complex, then the result is {[[unitary]] [[upper-triangular]]} SIZE(matrix) Dimensions of matrix returned as a list (rows, columns) SPECNORM(matrix) Spectral norm of a matrix SPECRAD(matrix) Spectral radius of a square matrix SVD(matrix) Singular value decomposition: factors an m x n matrix into two matrices and a vector {[[m x m square orthogonal]], [[n x n square orthogonal]], and [real]} SVL(matrix) Singular values: returns a vector containing the singular value of a matrix TRACE(matrix) Finds the trace of a square matrix. The trace is equal to the sum of the diagonal elements (it is also equal to the sum of the eigenvalues) TRN(matrix) Transposes matrix: for a complex matrix, TRN finds the conjugate transpose

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