Geometric significance of eigenvectors of greater sized co-variance matrix of a rectangular matrix
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I have a set of, say 100, 3d points. In the matrix form I keep it as 3 X 100 sized rectangular, named M (3 X 100 ), matrix
I calculate two co-variance matrices, one of size 3 X 3 [ M * Transpose(M)] and the other of size 100 X 100 [ Transpose(M) * M ]. I know that the geometric significance of the eigenvectors of the co-variance matrix of size 3 X 3 [ M * Transpose(M)] is the principal basis (orthonormal) vectors along which the 100 given points are spread (PCA) in the 3 mutually perpendicular directions.
What is then the geometric significance of the eigenvectors of the other co-variance matrix whose size is 100 X 100 [ Transpose(M) * M ]?
eigenvalues-eigenvectors
asked Jan 5 at 13:22
Parthasarathy SRINIVASANParthasarathy SRINIVASAN
63
$endgroup$
add a comment |
$begingroup$
I have a set of, say 100, 3d points. In the matrix form I keep it as 3 X 100 sized rectangular, named M (3 X 100 ), matrix
I calculate two co-variance matrices, one of size 3 X 3 [ M * Transpose(M)] and the other of size 100 X 100 [ Transpose(M) * M ]. I know that the geometric significance of the eigenvectors of the co-variance matrix of size 3 X 3 [ M * Transpose(M)] is the principal basis (orthonormal) vectors along which the 100 given points are spread (PCA) in the 3 mutually perpendicular directions.
What is then the geometric significance of the eigenvectors of the other co-variance matrix whose size is 100 X 100 [ Transpose(M) * M ]?
eigenvalues-eigenvectors
asked Jan 5 at 13:22
Parthasarathy SRINIVASANParthasarathy SRINIVASAN
63
$endgroup$
add a comment |
$begingroup$
I have a set of, say 100, 3d points. In the matrix form I keep it as 3 X 100 sized rectangular, named M (3 X 100 ), matrix
I calculate two co-variance matrices, one of size 3 X 3 [ M * Transpose(M)] and the other of size 100 X 100 [ Transpose(M) * M ]. I know that the geometric significance of the eigenvectors of the co-variance matrix of size 3 X 3 [ M * Transpose(M)] is the principal basis (orthonormal) vectors along which the 100 given points are spread (PCA) in the 3 mutually perpendicular directions.
What is then the geometric significance of the eigenvectors of the other co-variance matrix whose size is 100 X 100 [ Transpose(M) * M ]?
eigenvalues-eigenvectors
asked Jan 5 at 13:22
Parthasarathy SRINIVASANParthasarathy SRINIVASAN
63
$endgroup$
I have a set of, say 100, 3d points. In the matrix form I keep it as 3 X 100 sized rectangular, named M (3 X 100 ), matrix
I calculate two co-variance matrices, one of size 3 X 3 [ M * Transpose(M)] and the other of size 100 X 100 [ Transpose(M) * M ]. I know that the geometric significance of the eigenvectors of the co-variance matrix of size 3 X 3 [ M * Transpose(M)] is the principal basis (orthonormal) vectors along which the 100 given points are spread (PCA) in the 3 mutually perpendicular directions.
What is then the geometric significance of the eigenvectors of the other co-variance matrix whose size is 100 X 100 [ Transpose(M) * M ]?
eigenvalues-eigenvectors
eigenvalues-eigenvectors
asked Jan 5 at 13:22
Parthasarathy SRINIVASANParthasarathy SRINIVASAN
63
asked Jan 5 at 13:22
Parthasarathy SRINIVASANParthasarathy SRINIVASAN
63
edited Jan 5 at 13:27
Parthasarathy SRINIVASAN
asked Jan 5 at 13:22
Parthasarathy SRINIVASANParthasarathy SRINIVASAN
63
asked Jan 5 at 13:22
Parthasarathy SRINIVASANParthasarathy SRINIVASAN
63
asked Jan 5 at 13:22
Parthasarathy SRINIVASANParthasarathy SRINIVASAN
63
63
add a comment |
add a comment |
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