Main Content

inv

Inverse of symbolic matrix

Description

example

D = inv(A) returns the inverse of the square matrix of symbolic scalar variables A.

D = inv(M) returns the inverse of the square symbolic matrix variable M. (since R2021b)

Examples

collapse all

Compute the inverse of a matrix of symbolic numbers.

A = sym([2 -1 0; -1 2 -1; 0 -1 2]);
D = inv(A)
D = 

(34121412112141234)

Compute the inverse of a matrix of symbolic scalar variables.

syms a b c d
A = [a b; c d];
D = inv(A)
D = 

(dad-bc-bad-bc-cad-bcaad-bc)

Compute the inverse of the Hilbert matrix that contains symbolic numbers.

D = inv(sym(hilb(4)))
D = 

(16-120240-140-1201200-27001680240-27006480-4200-1401680-42002800)

Since R2021b

Find the inverse of a 4-by-4 block matrix

C=[A00B]

where A and B are 2-by-2 submatrices. The notation 0 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 = 02,2
C = [A Z; Z B]
C = 

(A02,202,2B)

Find the inverse of the matrix C.

D = inv(C)
D = 

(A02,202,2B)-1

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 = 

(A2,2σ2-A1,2σ200-A2,1σ2A1,1σ20000B2,2σ1-B1,2σ100-B2,1σ1B1,1σ1)where  σ1=B1,1B2,2-B1,2B2,1  σ2=A1,1A2,2-A1,2A2,1

Input Arguments

collapse all

Input matrix, specified as a square numeric matrix or matrix of symbolic matrix variables.

Data Types: single | double | sym

Since R2021b

Input matrix, specified as a square symbolic matrix variable.

Data Types: symmatrix

Limitations

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.

See Also

| |

Introduced before R2006a