LINEAR VECTOR SPACE DERIVATION OF NEW EXPRESSIONS FOR THE PSEUDO INVERSE OF RECTANGULAR MATRICES
Fuente:
Redalyc
Saved in:
| Main Author: | |
|---|---|
| Format: | Artículo científico |
| Language: | en |
| Published: |
Universidad Nacional Autónoma de México
2007
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1876461337104613376 |
|---|---|
| author | Marco Antonio Murray Lasso |
| author_facet | Marco Antonio Murray Lasso |
| contents | LINEAR VECTOR SPACE DERIVATION OF NEW EXPRESSIONS FOR THE PSEUDO INVERSE OF RECTANGULAR MATRICES Marco Antonio Murray Lasso Ingeniería Pseudo inverse generalized inverse linear vector spaces least square solutions orthogonal projections In this paper, a family of simple formulas for the calculation of the pseudo inverse of a rectangular matrix of less than maximum rank is derived using linear vector space methods. The principal result is that the pseudo inverse A+ of a matrix A can be calculated as A+ = Q(PTAQ)-1PT, where P and Q are rectangular matrices whose r columns are vectors that form a basis for the spaces spanned by the columns and rows, respectively, of matrix A. This leaves the user the liberty to choose the basis to take into consideration other questions such as amount of work needed and ill-conditioning of the matrix that has to be inverted. The formulas are particularized for rectangular matrices that have maximum rank and for the trivial case in which the original matrix is non-singular. Illustrative numerical examples are worked out for several choices of basis vectors and the results are compared with those provided by the program Mathematica through its function PseudoInverse[A]. 2007 artículo científico 1665-6423 https://www.redalyc.org/articulo.oa?id=47411541002 en http://www.redalyc.org/revista.oa?id=474 Journal of Applied Research and Technology application/pdf Universidad Nacional Autónoma de México Journal of Applied Research and Technology (México) Num.3 Vol.5 |
| format | Artículo científico |
| id | redalyc_47411541002 |
| institution | Redalyc |
| language | en |
| publishDate | 2007 |
| publisher | Universidad Nacional Autónoma de México |
| spellingShingle | LINEAR VECTOR SPACE DERIVATION OF NEW EXPRESSIONS FOR THE PSEUDO INVERSE OF RECTANGULAR MATRICES Marco Antonio Murray Lasso Ingeniería Pseudo inverse generalized inverse linear vector spaces least square solutions orthogonal projections LINEAR VECTOR SPACE DERIVATION OF NEW EXPRESSIONS FOR THE PSEUDO INVERSE OF RECTANGULAR MATRICES Marco Antonio Murray Lasso Ingeniería Pseudo inverse generalized inverse linear vector spaces least square solutions orthogonal projections In this paper, a family of simple formulas for the calculation of the pseudo inverse of a rectangular matrix of less than maximum rank is derived using linear vector space methods. The principal result is that the pseudo inverse A+ of a matrix A can be calculated as A+ = Q(PTAQ)-1PT, where P and Q are rectangular matrices whose r columns are vectors that form a basis for the spaces spanned by the columns and rows, respectively, of matrix A. This leaves the user the liberty to choose the basis to take into consideration other questions such as amount of work needed and ill-conditioning of the matrix that has to be inverted. The formulas are particularized for rectangular matrices that have maximum rank and for the trivial case in which the original matrix is non-singular. Illustrative numerical examples are worked out for several choices of basis vectors and the results are compared with those provided by the program Mathematica through its function PseudoInverse[A]. 2007 artículo científico 1665-6423 https://www.redalyc.org/articulo.oa?id=47411541002 en http://www.redalyc.org/revista.oa?id=474 Journal of Applied Research and Technology application/pdf Universidad Nacional Autónoma de México Journal of Applied Research and Technology (México) Num.3 Vol.5 |
| title | LINEAR VECTOR SPACE DERIVATION OF NEW EXPRESSIONS FOR THE PSEUDO INVERSE OF RECTANGULAR MATRICES |
| topic | Ingeniería Pseudo inverse generalized inverse linear vector spaces least square solutions orthogonal projections |
| url | https://www.redalyc.org/articulo.oa?id=47411541002 |