Symbolic Math Toolbox

inv

Matrix inverse

Syntax

• R = inv(A)
  

Description

inv(A) returns inverse of the symbolic matrix A.

Examples

The statements

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

return

• [ 3/4, 1/2, 1/4]
  [ 1/2,   1, 1/2]
  [ 1/4, 1/2, 3/4]
  

The statements

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

return

• [  d/(a*d-b*c), -b/(a*d-b*c)]
  [ -c/(a*d-b*c),  a/(a*d-b*c)]
  

Suppose you have created the following M-file.

• %% Generate a symbolic N-by-N Hilbert matrix.
  function A = genhilb(N)
  syms t;
  for i = 1:N
          for j = 1:N
          A(i,j) = 1/(i + j - t);
          end
  end
  

Then, the following statement

• inv(genhilb(2))
  

returns

• [    -(-3+t)^2*(-2+t), (-3+t)*(-2+t)*(-4+t)] 
  [(-3+t)*(-2+t)*(-4+t),     -(-3+t)^2*(-4+t)] 
  

the symbolic inverse of the 2-by-2 Hilbert matrix.

See Also

vpa

Arithmetic Operations page

int

iztrans