How to find the singular values associated with the largest singular value
0
I have a rectangular complex matrix, and I require to compute the singular vectors (first row and first column) associated with the largest singular value without computing the full SVD decomposition. Can someone indicate what steps should I follow, or refer me to relevant literature?
linear-algebra matrices optimization signal-processing
asked Nov 26 at 10:42
Fer Nando
164
add a comment |
0
I have a rectangular complex matrix, and I require to compute the singular vectors (first row and first column) associated with the largest singular value without computing the full SVD decomposition. Can someone indicate what steps should I follow, or refer me to relevant literature?
linear-algebra matrices optimization signal-processing
asked Nov 26 at 10:42
Fer Nando
164
Multiply the rectangular matrix by its conjugate transpose to generate a square (aka cross-product) matrix, then apply Power Iteration to find its greatest eigenvalue. The eigenvalues of the cross-product matrix equal the singular values of the original matrix.
– greg
Nov 26 at 14:51
Thank you for your reply. I need to find the singular vectors associated with the largest singular value.
– Fer Nando
Nov 26 at 15:53
Power Iteration also yields the eigenvector associated with the dominant eigenvalue. The dominant eigenvectors of $AA^*$ and of $A^*A$ correspond to the columns of $(U,V)$ associated with the dominant singular value, i.e. $A=USV^*$.
– greg
Nov 26 at 22:06
Thank you again for your reply.
– Fer Nando
Nov 27 at 5:57
add a comment |
0
0
0
I have a rectangular complex matrix, and I require to compute the singular vectors (first row and first column) associated with the largest singular value without computing the full SVD decomposition. Can someone indicate what steps should I follow, or refer me to relevant literature?
linear-algebra matrices optimization signal-processing
asked Nov 26 at 10:42
Fer Nando
164
I have a rectangular complex matrix, and I require to compute the singular vectors (first row and first column) associated with the largest singular value without computing the full SVD decomposition. Can someone indicate what steps should I follow, or refer me to relevant literature?
linear-algebra matrices optimization signal-processing
linear-algebra matrices optimization signal-processing
asked Nov 26 at 10:42
Fer Nando
164
asked Nov 26 at 10:42
Fer Nando
164
asked Nov 26 at 10:42
Fer Nando
164
asked Nov 26 at 10:42
Fer Nando
164
asked Nov 26 at 10:42
Fer Nando
164
164
Multiply the rectangular matrix by its conjugate transpose to generate a square (aka cross-product) matrix, then apply Power Iteration to find its greatest eigenvalue. The eigenvalues of the cross-product matrix equal the singular values of the original matrix.
– greg
Nov 26 at 14:51
Thank you for your reply. I need to find the singular vectors associated with the largest singular value.
– Fer Nando
Nov 26 at 15:53
Power Iteration also yields the eigenvector associated with the dominant eigenvalue. The dominant eigenvectors of $AA^*$ and of $A^*A$ correspond to the columns of $(U,V)$ associated with the dominant singular value, i.e. $A=USV^*$.
– greg
Nov 26 at 22:06
Thank you again for your reply.
– Fer Nando
Nov 27 at 5:57
add a comment |
Multiply the rectangular matrix by its conjugate transpose to generate a square (aka cross-product) matrix, then apply Power Iteration to find its greatest eigenvalue. The eigenvalues of the cross-product matrix equal the singular values of the original matrix.
– greg
Nov 26 at 14:51
Thank you for your reply. I need to find the singular vectors associated with the largest singular value.
– Fer Nando
Nov 26 at 15:53
Power Iteration also yields the eigenvector associated with the dominant eigenvalue. The dominant eigenvectors of $AA^*$ and of $A^*A$ correspond to the columns of $(U,V)$ associated with the dominant singular value, i.e. $A=USV^*$.
– greg
Nov 26 at 22:06
Thank you again for your reply.
– Fer Nando
Nov 27 at 5:57
Multiply the rectangular matrix by its conjugate transpose to generate a square (aka cross-product) matrix, then apply Power Iteration to find its greatest eigenvalue. The eigenvalues of the cross-product matrix equal the singular values of the original matrix.
– greg
Nov 26 at 14:51
Multiply the rectangular matrix by its conjugate transpose to generate a square (aka cross-product) matrix, then apply Power Iteration to find its greatest eigenvalue. The eigenvalues of the cross-product matrix equal the singular values of the original matrix.
– greg
Nov 26 at 14:51
Thank you for your reply. I need to find the singular vectors associated with the largest singular value.
– Fer Nando
Nov 26 at 15:53
Thank you for your reply. I need to find the singular vectors associated with the largest singular value.
– Fer Nando
Nov 26 at 15:53
Power Iteration also yields the eigenvector associated with the dominant eigenvalue. The dominant eigenvectors of $AA^*$ and of $A^*A$ correspond to the columns of $(U,V)$ associated with the dominant singular value, i.e. $A=USV^*$.
– greg
Nov 26 at 22:06
Power Iteration also yields the eigenvector associated with the dominant eigenvalue. The dominant eigenvectors of $AA^*$ and of $A^*A$ correspond to the columns of $(U,V)$ associated with the dominant singular value, i.e. $A=USV^*$.
– greg
Nov 26 at 22:06
Thank you again for your reply.
– Fer Nando
Nov 27 at 5:57
Thank you again for your reply.
– Fer Nando
Nov 27 at 5:57
add a comment |
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Multiply the rectangular matrix by its conjugate transpose to generate a square (aka cross-product) matrix, then apply Power Iteration to find its greatest eigenvalue. The eigenvalues of the cross-product matrix equal the singular values of the original matrix.
– greg
Nov 26 at 14:51
Thank you for your reply. I need to find the singular vectors associated with the largest singular value.
– Fer Nando
Nov 26 at 15:53
Power Iteration also yields the eigenvector associated with the dominant eigenvalue. The dominant eigenvectors of $AA^*$ and of $A^*A$ correspond to the columns of $(U,V)$ associated with the dominant singular value, i.e. $A=USV^*$.
– greg
Nov 26 at 22:06
Thank you again for your reply.
– Fer Nando
Nov 27 at 5:57