Why are the eigenvalues of eig() sorted in ascending order?
I'm trying to find eigenvalues of a matrix with eig.
I define the matrix with example data:
A = magic(5)
A =
17 24 1 8 15
23 5 7 14 16
4 6 13 20 22
10 12 19 21 3
11 18 25 2 9
and
D = eig(A,'matrix')
D =
65.0000 0 0 0 0
0 -21.2768 0 0 0
0 0 -13.1263 0 0
0 0 0 21.2768 0
0 0 0 0 13.1263
But if I use
C = cov(A)
and get eigenvalues from the covariance matrix, this is the result:
DC = eig(C,'matrix')
DC =
-0.0000 0 0 0 0
0 35.4072 0 0 0
0 0 44.9139 0 0
0 0 0 117.5861 0
0 0 0 0 127.0928
Why are the eigenvalues from the covariance matrix sorted in ascending order?
matlab matrix linear-algebra pca eigenvalue
edited Nov 27 '18 at 15:46
Adriaan
12.9k63162
asked Nov 27 '18 at 15:36
Wanarase Cs SinhashthitaWanarase Cs Sinhashthita
132
add a comment |
I'm trying to find eigenvalues of a matrix with eig.
I define the matrix with example data:
A = magic(5)
A =
17 24 1 8 15
23 5 7 14 16
4 6 13 20 22
10 12 19 21 3
11 18 25 2 9
and
D = eig(A,'matrix')
D =
65.0000 0 0 0 0
0 -21.2768 0 0 0
0 0 -13.1263 0 0
0 0 0 21.2768 0
0 0 0 0 13.1263
But if I use
C = cov(A)
and get eigenvalues from the covariance matrix, this is the result:
DC = eig(C,'matrix')
DC =
-0.0000 0 0 0 0
0 35.4072 0 0 0
0 0 44.9139 0 0
0 0 0 117.5861 0
0 0 0 0 127.0928
Why are the eigenvalues from the covariance matrix sorted in ascending order?
matlab matrix linear-algebra pca eigenvalue
edited Nov 27 '18 at 15:46
Adriaan
12.9k63162
asked Nov 27 '18 at 15:36
Wanarase Cs SinhashthitaWanarase Cs Sinhashthita
132
Related. Duplicate?
– Luis Mendo
Nov 27 '18 at 16:03
add a comment |
I'm trying to find eigenvalues of a matrix with eig.
I define the matrix with example data:
A = magic(5)
A =
17 24 1 8 15
23 5 7 14 16
4 6 13 20 22
10 12 19 21 3
11 18 25 2 9
and
D = eig(A,'matrix')
D =
65.0000 0 0 0 0
0 -21.2768 0 0 0
0 0 -13.1263 0 0
0 0 0 21.2768 0
0 0 0 0 13.1263
But if I use
C = cov(A)
and get eigenvalues from the covariance matrix, this is the result:
DC = eig(C,'matrix')
DC =
-0.0000 0 0 0 0
0 35.4072 0 0 0
0 0 44.9139 0 0
0 0 0 117.5861 0
0 0 0 0 127.0928
Why are the eigenvalues from the covariance matrix sorted in ascending order?
matlab matrix linear-algebra pca eigenvalue
edited Nov 27 '18 at 15:46
Adriaan
12.9k63162
asked Nov 27 '18 at 15:36
Wanarase Cs SinhashthitaWanarase Cs Sinhashthita
132
I'm trying to find eigenvalues of a matrix with eig.
I define the matrix with example data:
A = magic(5)
A =
17 24 1 8 15
23 5 7 14 16
4 6 13 20 22
10 12 19 21 3
11 18 25 2 9
and
D = eig(A,'matrix')
D =
65.0000 0 0 0 0
0 -21.2768 0 0 0
0 0 -13.1263 0 0
0 0 0 21.2768 0
0 0 0 0 13.1263
But if I use
C = cov(A)
and get eigenvalues from the covariance matrix, this is the result:
DC = eig(C,'matrix')
DC =
-0.0000 0 0 0 0
0 35.4072 0 0 0
0 0 44.9139 0 0
0 0 0 117.5861 0
0 0 0 0 127.0928
Why are the eigenvalues from the covariance matrix sorted in ascending order?
matlab matrix linear-algebra pca eigenvalue
matlab matrix linear-algebra pca eigenvalue
edited Nov 27 '18 at 15:46
Adriaan
12.9k63162
asked Nov 27 '18 at 15:36
Wanarase Cs SinhashthitaWanarase Cs Sinhashthita
132
edited Nov 27 '18 at 15:46
Adriaan
12.9k63162
asked Nov 27 '18 at 15:36
Wanarase Cs SinhashthitaWanarase Cs Sinhashthita
132
edited Nov 27 '18 at 15:46
Adriaan
12.9k63162
edited Nov 27 '18 at 15:46
Adriaan
12.9k63162
edited Nov 27 '18 at 15:46
Adriaan
12.9k63162
12.9k63162
asked Nov 27 '18 at 15:36
Wanarase Cs SinhashthitaWanarase Cs Sinhashthita
132
asked Nov 27 '18 at 15:36
Wanarase Cs SinhashthitaWanarase Cs Sinhashthita
132
asked Nov 27 '18 at 15:36
Wanarase Cs SinhashthitaWanarase Cs Sinhashthita
132
132
Related. Duplicate?
– Luis Mendo
Nov 27 '18 at 16:03
add a comment |
Related. Duplicate?
– Luis Mendo
Nov 27 '18 at 16:03
Related. Duplicate?
– Luis Mendo
Nov 27 '18 at 16:03
Related. Duplicate?
– Luis Mendo
Nov 27 '18 at 16:03
add a comment |
1 Answer
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oldest
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Sorting is merely a choice of convenience. There's no such thing as a 'real' position of an eigenvector, just as (x,y) is just as valid as (y,x). Since a lot of matrix techniques work on eigenvectors in order of decreasing eigenvalue (i.e. most important first), it makes sense to structure them accordingly.
answered Nov 27 '18 at 15:45
AdriaanAdriaan
12.9k63162
add a comment |
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1 Answer
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sorting is merely a choice of convenience. There's no such thing as a 'real' position of an eigenvector, just as (x,y) is just as valid as (y,x). Since a lot of matrix techniques work on eigenvectors in order of decreasing eigenvalue (i.e. most important first), it makes sense to structure them accordingly.
answered Nov 27 '18 at 15:45
AdriaanAdriaan
12.9k63162
add a comment |
Sorting is merely a choice of convenience. There's no such thing as a 'real' position of an eigenvector, just as (x,y) is just as valid as (y,x). Since a lot of matrix techniques work on eigenvectors in order of decreasing eigenvalue (i.e. most important first), it makes sense to structure them accordingly.
answered Nov 27 '18 at 15:45
AdriaanAdriaan
12.9k63162
add a comment |
Sorting is merely a choice of convenience. There's no such thing as a 'real' position of an eigenvector, just as (x,y) is just as valid as (y,x). Since a lot of matrix techniques work on eigenvectors in order of decreasing eigenvalue (i.e. most important first), it makes sense to structure them accordingly.
answered Nov 27 '18 at 15:45
AdriaanAdriaan
12.9k63162
Sorting is merely a choice of convenience. There's no such thing as a 'real' position of an eigenvector, just as (x,y) is just as valid as (y,x). Since a lot of matrix techniques work on eigenvectors in order of decreasing eigenvalue (i.e. most important first), it makes sense to structure them accordingly.
answered Nov 27 '18 at 15:45
AdriaanAdriaan
12.9k63162
answered Nov 27 '18 at 15:45
AdriaanAdriaan
12.9k63162
answered Nov 27 '18 at 15:45
AdriaanAdriaan
12.9k63162
answered Nov 27 '18 at 15:45
AdriaanAdriaan
12.9k63162
12.9k63162
add a comment |
add a comment |
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Related. Duplicate?
– Luis Mendo
Nov 27 '18 at 16:03