PRODUCTS
Mathematica
Mathematica for Students
Mathematica for the Classroom
Mathematica Personal Grid Edition
grid
Mathematica
web
Mathematica
Mathematica Player
(free download)
Mathematica Player Pro
Wolfram
Workbench
Mathematica
Applications
PURCHASE
Online Store
Other Ways to Buy
Volume & Site Licensing
Contact Sales
Software
Service
Upgrades
Training
Books
FOR USERS
All User Resources
Product Registration
Technical Support
Customer Service
Developer Support
Does My Site Have a License?
Free Seminars
Certified Training
Documentation & Examples
Tutorial Screencasts
Video Gallery
Demonstrations Project
Education Portal
Student Resources
COMPANY
About Wolfram Research
News & Events
Wolfram Blog
Employment Opportunities
History of
Mathematica
Stephen Wolfram's Home Page
Contact Us
OUR SITES
Demonstrations Project
MathWorld
Integrator
Wolfram Functions Site
Wolfram Blog
Mathematica Journal
Wolfram Library Archive
Wolfram
Tones
Wolfram Science
Stephen Wolfram
DOCUMENTATION CENTER SEARCH
Mathematica
>
Matrix-Based Minimization
>
Built-in
Mathematica
Symbol
Advanced Matrix Operations
Tutorials »
|
Inverse
LeastSquares
Fit
SingularValueDecomposition
SingularValueList
See Also »
|
Linear Systems
Matrices and Linear Algebra
Matrix-Based Minimization
More About »
PseudoInverse
PseudoInverse
[
m
]
finds the pseudoinverse of a rectangular matrix.
MORE INFORMATION
PseudoInverse
works on both symbolic and numerical matrices.
For a square matrix,
PseudoInverse
gives the Moore-Penrose inverse.
For numerical matrices,
PseudoInverse
is based on
SingularValueDecomposition
.
PseudoInverse
[
m
,
Tolerance
->
t
]
specifies that singular values smaller than
t
times the maximum singular value should be dropped.
With the default setting
Tolerance
->
Automatic
, singular values are dropped when they are less than 100 times
10
-
p
, where
p
is
Precision
[
m
]
.
For non-singular square matrices
M
, the pseudoinverse
M
(-1)
is equivalent to the standard inverse.
EXAMPLES
CLOSE ALL
Basic Examples
(1)
A matrix has a pseudoinverse even if it is singular:
In[1]:=
Out[1]=
Scope
(2)
Generalizations & Extensions
(1)
Options
(1)
Applications
(1)
Properties & Relations
(3)
SEE ALSO
Inverse
LeastSquares
Fit
SingularValueDecomposition
SingularValueList
TUTORIALS
Advanced Matrix Operations
MORE ABOUT
Linear Systems
Matrices and Linear Algebra
Matrix-Based Minimization
RELATED LINKS
NKS|Online
(
A New Kind of Science
)
New in 1 | Last modified in 5
© 2008 Wolfram Research, Inc.