Eigen-decomposition of real Symmetric psd matrix
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I am doing PCA analysis on a large amount of data and I need to compute the eigen-decomposition of the covariance matrix which is a real, symmetric, positive semi definite matrix. It doesn't get any simpler than that!
I want to compute this myself from first principles and not using some matlab, mathematica or whatever package. That's an infinite process but I am looking for a fast and robust method. Can anyone post an algorithm for it? I did a web search and found several methods but nothing complete and from scratch.
Please help, thanks in advance.
linear-algebra matrices eigenvalues-eigenvectors linear-transformations singularvalues
asked Dec 4 '18 at 9:17
plus1plus1
3911
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add a comment |
$begingroup$
I am doing PCA analysis on a large amount of data and I need to compute the eigen-decomposition of the covariance matrix which is a real, symmetric, positive semi definite matrix. It doesn't get any simpler than that!
I want to compute this myself from first principles and not using some matlab, mathematica or whatever package. That's an infinite process but I am looking for a fast and robust method. Can anyone post an algorithm for it? I did a web search and found several methods but nothing complete and from scratch.
Please help, thanks in advance.
linear-algebra matrices eigenvalues-eigenvectors linear-transformations singularvalues
asked Dec 4 '18 at 9:17
plus1plus1
3911
$endgroup$
$begingroup$
You will find answer to it and many others in a best seller, very often cited in scientific papers: "Matrix Computations" by Golub and Van Loan. I know that listing books may lead to an endless dangerous chat, but this book is special ...
$endgroup$
– Damien
Dec 4 '18 at 9:29
1
$begingroup$
I want to reinvent a wheel but have no idea what a wheel looks like, can you post one? I'm impressed by your resolute denial of computer codes people worked on for decades, sir.
$endgroup$
– Algebraic Pavel
Dec 4 '18 at 9:40
$begingroup$
@AlgebraicPavel Sometimes, when you are doing research, you are not only interested in the functionality of a program, but you want to deeply understand it. And sometimes, the benefit of such a deep understanding of a given function appear a long time after, in an unexpected way.
$endgroup$
– Damien
Dec 4 '18 at 10:02
$begingroup$
@Damien I understand that what you say might be happening but the question does not give me an impression that this is the case.
$endgroup$
– Algebraic Pavel
Dec 4 '18 at 10:55
$begingroup$
@Damien Thanks! It's quite involved with bidiagonal matrices and so on but it looks like I can't do any better...
$endgroup$
– plus1
Dec 4 '18 at 11:10
add a comment |
$begingroup$
I am doing PCA analysis on a large amount of data and I need to compute the eigen-decomposition of the covariance matrix which is a real, symmetric, positive semi definite matrix. It doesn't get any simpler than that!
I want to compute this myself from first principles and not using some matlab, mathematica or whatever package. That's an infinite process but I am looking for a fast and robust method. Can anyone post an algorithm for it? I did a web search and found several methods but nothing complete and from scratch.
Please help, thanks in advance.
linear-algebra matrices eigenvalues-eigenvectors linear-transformations singularvalues
asked Dec 4 '18 at 9:17
plus1plus1
3911
$endgroup$
I am doing PCA analysis on a large amount of data and I need to compute the eigen-decomposition of the covariance matrix which is a real, symmetric, positive semi definite matrix. It doesn't get any simpler than that!
I want to compute this myself from first principles and not using some matlab, mathematica or whatever package. That's an infinite process but I am looking for a fast and robust method. Can anyone post an algorithm for it? I did a web search and found several methods but nothing complete and from scratch.
Please help, thanks in advance.
linear-algebra matrices eigenvalues-eigenvectors linear-transformations singularvalues
linear-algebra matrices eigenvalues-eigenvectors linear-transformations singularvalues
asked Dec 4 '18 at 9:17
plus1plus1
3911
asked Dec 4 '18 at 9:17
plus1plus1
3911
asked Dec 4 '18 at 9:17
plus1plus1
3911
asked Dec 4 '18 at 9:17
plus1plus1
3911
asked Dec 4 '18 at 9:17
plus1plus1
3911
3911
$begingroup$
You will find answer to it and many others in a best seller, very often cited in scientific papers: "Matrix Computations" by Golub and Van Loan. I know that listing books may lead to an endless dangerous chat, but this book is special ...
$endgroup$
– Damien
Dec 4 '18 at 9:29
1
$begingroup$
I want to reinvent a wheel but have no idea what a wheel looks like, can you post one? I'm impressed by your resolute denial of computer codes people worked on for decades, sir.
$endgroup$
– Algebraic Pavel
Dec 4 '18 at 9:40
$begingroup$
@AlgebraicPavel Sometimes, when you are doing research, you are not only interested in the functionality of a program, but you want to deeply understand it. And sometimes, the benefit of such a deep understanding of a given function appear a long time after, in an unexpected way.
$endgroup$
– Damien
Dec 4 '18 at 10:02
$begingroup$
@Damien I understand that what you say might be happening but the question does not give me an impression that this is the case.
$endgroup$
– Algebraic Pavel
Dec 4 '18 at 10:55
$begingroup$
@Damien Thanks! It's quite involved with bidiagonal matrices and so on but it looks like I can't do any better...
$endgroup$
– plus1
Dec 4 '18 at 11:10
add a comment |
$begingroup$
You will find answer to it and many others in a best seller, very often cited in scientific papers: "Matrix Computations" by Golub and Van Loan. I know that listing books may lead to an endless dangerous chat, but this book is special ...
$endgroup$
– Damien
Dec 4 '18 at 9:29
1
$begingroup$
I want to reinvent a wheel but have no idea what a wheel looks like, can you post one? I'm impressed by your resolute denial of computer codes people worked on for decades, sir.
$endgroup$
– Algebraic Pavel
Dec 4 '18 at 9:40
$begingroup$
@AlgebraicPavel Sometimes, when you are doing research, you are not only interested in the functionality of a program, but you want to deeply understand it. And sometimes, the benefit of such a deep understanding of a given function appear a long time after, in an unexpected way.
$endgroup$
– Damien
Dec 4 '18 at 10:02
$begingroup$
@Damien I understand that what you say might be happening but the question does not give me an impression that this is the case.
$endgroup$
– Algebraic Pavel
Dec 4 '18 at 10:55
$begingroup$
@Damien Thanks! It's quite involved with bidiagonal matrices and so on but it looks like I can't do any better...
$endgroup$
– plus1
Dec 4 '18 at 11:10
$begingroup$
You will find answer to it and many others in a best seller, very often cited in scientific papers: "Matrix Computations" by Golub and Van Loan. I know that listing books may lead to an endless dangerous chat, but this book is special ...
$endgroup$
– Damien
Dec 4 '18 at 9:29
$begingroup$
You will find answer to it and many others in a best seller, very often cited in scientific papers: "Matrix Computations" by Golub and Van Loan. I know that listing books may lead to an endless dangerous chat, but this book is special ...
$endgroup$
– Damien
Dec 4 '18 at 9:29
1
1
$begingroup$
I want to reinvent a wheel but have no idea what a wheel looks like, can you post one? I'm impressed by your resolute denial of computer codes people worked on for decades, sir.
$endgroup$
– Algebraic Pavel
Dec 4 '18 at 9:40
$begingroup$
I want to reinvent a wheel but have no idea what a wheel looks like, can you post one? I'm impressed by your resolute denial of computer codes people worked on for decades, sir.
$endgroup$
– Algebraic Pavel
Dec 4 '18 at 9:40
$begingroup$
@AlgebraicPavel Sometimes, when you are doing research, you are not only interested in the functionality of a program, but you want to deeply understand it. And sometimes, the benefit of such a deep understanding of a given function appear a long time after, in an unexpected way.
$endgroup$
– Damien
Dec 4 '18 at 10:02
$begingroup$
@AlgebraicPavel Sometimes, when you are doing research, you are not only interested in the functionality of a program, but you want to deeply understand it. And sometimes, the benefit of such a deep understanding of a given function appear a long time after, in an unexpected way.
$endgroup$
– Damien
Dec 4 '18 at 10:02
$begingroup$
@Damien I understand that what you say might be happening but the question does not give me an impression that this is the case.
$endgroup$
– Algebraic Pavel
Dec 4 '18 at 10:55
$begingroup$
@Damien I understand that what you say might be happening but the question does not give me an impression that this is the case.
$endgroup$
– Algebraic Pavel
Dec 4 '18 at 10:55
$begingroup$
@Damien Thanks! It's quite involved with bidiagonal matrices and so on but it looks like I can't do any better...
$endgroup$
– plus1
Dec 4 '18 at 11:10
$begingroup$
@Damien Thanks! It's quite involved with bidiagonal matrices and so on but it looks like I can't do any better...
$endgroup$
– plus1
Dec 4 '18 at 11:10
add a comment |
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$begingroup$
You will find answer to it and many others in a best seller, very often cited in scientific papers: "Matrix Computations" by Golub and Van Loan. I know that listing books may lead to an endless dangerous chat, but this book is special ...
$endgroup$
– Damien
Dec 4 '18 at 9:29
1
$begingroup$
I want to reinvent a wheel but have no idea what a wheel looks like, can you post one? I'm impressed by your resolute denial of computer codes people worked on for decades, sir.
$endgroup$
– Algebraic Pavel
Dec 4 '18 at 9:40
$begingroup$
@AlgebraicPavel Sometimes, when you are doing research, you are not only interested in the functionality of a program, but you want to deeply understand it. And sometimes, the benefit of such a deep understanding of a given function appear a long time after, in an unexpected way.
$endgroup$
– Damien
Dec 4 '18 at 10:02
$begingroup$
@Damien I understand that what you say might be happening but the question does not give me an impression that this is the case.
$endgroup$
– Algebraic Pavel
Dec 4 '18 at 10:55
$begingroup$
@Damien Thanks! It's quite involved with bidiagonal matrices and so on but it looks like I can't do any better...
$endgroup$
– plus1
Dec 4 '18 at 11:10