inv
Inverse of symbolic matrix
Syntax
Description
Examples
Compute Inverse of Symbolic Matrix
Compute the inverse of a matrix of symbolic numbers.
A = sym([2 -1 0; -1 2 -1; 0 -1 2]); D = inv(A)
D =
Compute the inverse of a matrix of symbolic scalar variables.
syms a b c d A = [a b; c d]; D = inv(A)
D =
Compute Inverse of Hilbert Matrix with Symbolic Numbers
Compute the inverse of the Hilbert matrix that contains symbolic numbers.
D = inv(sym(hilb(4)))
D =
Compute Inverse of Block Matrix
Find the inverse of a 4-by-4 block matrix
where and are 2-by-2 submatrices. The notation represents a 2-by-2 submatrix of zeros.
Use symbolic matrix variables to represent the submatrices in the block matrix.
syms A B [2 2] matrix Z = symmatrix(zeros(2))
Z =
C = [A Z; Z B]
C =
Find the inverse of the matrix .
D = inv(C)
D =
To show the elements of the inverse matrix, convert the result from a symbolic matrix variable to symbolic scalar variables using symmatrix2sym
.
D1 = symmatrix2sym(D)
D1 =
Compute Inverse of Matrix Polynomial
Compute the inverse of the matrix polynomial , where is a 2-by-2 matrix.
Create the matrix and the coefficients , , and as symbolic matrix variables. Create the matrix polynomial as a symbolic matrix function f
with , , , and as its parameters.
syms A [2 2] matrix syms a0 a1 a2 [1 1] matrix syms f(A,a0,a1,a2) [2 2] matrix keepargs f(A,a0,a1,a2) = a0*eye(2) + a1*A + a2*A^2
f(A, a0, a1, a2) =
Find the inverse of f
using inv
. The result is a symbolic matrix function of type symfunmatrix
.
fInv = inv(f)
fInv(A, a0, a1, a2) =
Evaluate the inverse for the matrix value and the coefficient values , , and . The result is a symbolic matrix variable of type symmatrix
.
Aval = [2 -1; -1 2]; fEval = fInv(Aval,-1,2,3)
fEval =
Convert the result from the symmatrix
data type to the sym
data type using symmatrix2sym
. The result is a matrix of symbolic numbers.
symmatrix2sym(fEval)
ans =
Input Arguments
A
— Input matrix
square numeric matrix | square matrix of symbolic scalar variables | square symbolic matrix variable | square symbolic matrix function | symbolic expression with square size
Input matrix, specified as a square numeric matrix, square matrix of symbolic scalar variables, square symbolic matrix variable, square symbolic matrix function, or symbolic expression with square size.
Data Types: single
| double
| sym
| symmatrix
| symfunmatrix
Tips
Matrix computations involving many symbolic variables can be slow. To increase the computational speed, reduce the number of symbolic variables by substituting the given values for some variables.
Version History
Introduced before R2006aR2022a: Compute inverse of symbolic matrix functions
The inv
function accepts an input argument of type
symfunmatrix
. For an example, see Compute Inverse of Matrix Polynomial.
R2021b: Compute inverse of symbolic matrix variables
The inv
function accepts an input argument of type
symmatrix
. For an example, see Compute Inverse of Block Matrix.
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