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Matrix inverse

It is seldom necessary to form the explicit inverse of a matrix. A frequent misuse of

`inv`

arises when solving the system of linear equations*Ax*=*b*. One way to solve the equation is with`x = inv(A)*b`

. A better way, from the standpoint of both execution time and numerical accuracy, is to use the matrix backslash operator`x = A\b`

. This produces the solution using Gaussian elimination, without explicitly forming the inverse. See`mldivide`

for further information.

`inv`

performs an LU decomposition of the
input matrix (or an LDL decomposition if the input matrix is Hermitian).
It then uses the results to form a linear system whose solution is
the matrix inverse `inv(X)`

. For sparse inputs, `inv(X)`

creates
a sparse identity matrix and uses backslash, `X\speye(size(X))`

.