pinv
Moore-Penrose pseudoinverse
Description
B = pinv(
returns the Moore-Penrose Pseudoinverse of matrix
A
)A
.
Examples
Input Arguments
More About
Tips
You can replace most uses of
pinv
applied to a vectorb
, as inpinv(A)*b
, withlsqminnorm(A,b)
to get the minimum-norm least-squares solution of a system of linear equations.lsqminnorm
is generally more efficient thanpinv
, and it also supports sparse matrices.
Algorithms
pinv
uses the singular value decomposition to form the
pseudoinverse of A
. Singular values along the diagonal of
S
that are smaller than tol
are treated as
zeros, and the representation of A
becomes:
The pseudoinverse of A
is then equal to:
Extended Capabilities
Version History
Introduced before R2006aSee Also
inv
| qr
| rank
| svd
| lsqminnorm
| decomposition