Matrix calculation syntax

Parent Previous Next

A matrix can be defined through a matrix calculation.


A matrix calculation can use all items allowed for a real calculation along with operations specific to matrices.


Reference to a matrix term :


A matrix calculation can use a reference of a term belonging to a matrix already defined. For instance, if A is a matrix 3x2, A(3,2) will refer to the first term of the third row of matrix A.


Sum and difference of two matrices :


If A and B are two matrices of the same dimension, A+B returns the matrix sum and A - B returns the difference matrix of A and B.


Product of two matrices :


If A is a matrix with n rows and p columns and B a matrix with p rows and q columns, A*B returns the matrix product of  A and B (matrix with n rows and q columns).


Inverse of a matrix :


if A is an invertible square matrix, A^(-1) returns the inverse matrix of A.


Power of a matrix :


If A is a matrix and n a positive integer, A^n returns the n power of matrix A. If n ≥ 256, the result doesn't exist


Determinant of a matrix :


If A is a square matrix, deter(A) refers to the determinant of A.


Transposed of a matrix :


If A is a matrix with n rows and p columns, transp(A) returns the transposed matrix of A (matrix with p rows et n columns).


Term to term inverse of a matrix :


If A is a matrix, inv(A) returns the matrix where each term of A is replaced by the inverse. If one of the terms of A is zero, the result doesn't exist.


Term to term product :


If A and B are two matrices of the same dimensions, dotmult(A, B) returns the matrix terms of which are the products of the matching terms of matrix A and B.


Division term by term :


If A and B are two matrices of the same dimensions and if all the terms of B are not null, A/B returns the matrix terms of which are the result of the division of A terms by the matching terms of matrix B.


Image through a predefined function :


For instance, if A is a matrix, cos(A) returns the matrix terms of which are the image of A terms through function cosinus.


Image through a user defined function :


If A is a matrix and f a user-defined real function, f(A) returns the matrix terms of which are the image of A terms through function f.


Addition of a constant :


If A is a matrix and k a real number, k + A ou A + k returns the matrix terms of which are the terms of A added with k.


Subtraction of a constant :


If A is a matrix and k a real number, A - k returns the matrix terms of which are the result of the substraction of A terms and k.


If k is a real number and A a matrix, k - A returns  the matrix terms of which are the result of the substraction of  k and A terms.


Multiplication by a constant :


If A is a matrix and k a number, k*A ou A*k returns the matrix terms of which are the result of the multiplicatio of A terms and k.


Division by a constant :


If A is a matrix and k a real number different from zero, A/k returns the matrix terms of which are the result of the division of A terms by k.


if k is a real number and A a matrix, k/A returns the matrix terms of which are the result of the division of  k by A terms. The result doesn't exist of one of A terms is zero.


Approximation by a rational fraction :


If a is a real number, frac(a) returns a matrix with one row and two columns. The first term of the returned matrix is the numerator of the approximated rational fraction of this number (with 10^(-12) uncertainty) and the second term is the denominator of the fraction.


If a is a one column matrix,  frac(a) returns a matrix with two columns, the first column containing the numerators and the second column the denominators of the approximated rational fractions of each term of matrix a.


If a is a one row matrix,  frac(a) returns a matrix with two rows, the first row containing the numerators and the second row the denominators of the approximated rational fractions of each term of matrix a.


To be noticed :


If the result of a matrix calculation A is a matrix of one row and one column, a reference of A in a matrix calculation will be considered as a real number.


To get the result of the determinant in a real calculation, use the tool provided in the calculation menu (expanding the calculation toolbar). The derminant will be the result of a macro-construction.