What can can be said about the sum of a positive semidefinite matrix rank M and a diagonal matrix rank...
Let's consider the matrix A which is a N dimensional real positive semi-definite square matrix of rank M with M < N and a N dimensional real diagonal matrix D. What can be said about the matrix B = A + D?
If M = N, it is easy to prove exploiting eigenvalue decomposition that B can be any real symmetric matrix. Now I would like to understand which kind of matrices B can be represented if A has rank M < N. If this matrix can be characterised for instance through their eigenvalue spectrum or other properties.
linear-algebra abstract-algebra matrices eigenvalues-eigenvectors diagonalization
asked Nov 29 at 10:06
Nik
214
add a comment |
Let's consider the matrix A which is a N dimensional real positive semi-definite square matrix of rank M with M < N and a N dimensional real diagonal matrix D. What can be said about the matrix B = A + D?
If M = N, it is easy to prove exploiting eigenvalue decomposition that B can be any real symmetric matrix. Now I would like to understand which kind of matrices B can be represented if A has rank M < N. If this matrix can be characterised for instance through their eigenvalue spectrum or other properties.
linear-algebra abstract-algebra matrices eigenvalues-eigenvectors diagonalization
asked Nov 29 at 10:06
Nik
214
add a comment |
Let's consider the matrix A which is a N dimensional real positive semi-definite square matrix of rank M with M < N and a N dimensional real diagonal matrix D. What can be said about the matrix B = A + D?
If M = N, it is easy to prove exploiting eigenvalue decomposition that B can be any real symmetric matrix. Now I would like to understand which kind of matrices B can be represented if A has rank M < N. If this matrix can be characterised for instance through their eigenvalue spectrum or other properties.
linear-algebra abstract-algebra matrices eigenvalues-eigenvectors diagonalization
asked Nov 29 at 10:06
Nik
214
Let's consider the matrix A which is a N dimensional real positive semi-definite square matrix of rank M with M < N and a N dimensional real diagonal matrix D. What can be said about the matrix B = A + D?
If M = N, it is easy to prove exploiting eigenvalue decomposition that B can be any real symmetric matrix. Now I would like to understand which kind of matrices B can be represented if A has rank M < N. If this matrix can be characterised for instance through their eigenvalue spectrum or other properties.
linear-algebra abstract-algebra matrices eigenvalues-eigenvectors diagonalization
linear-algebra abstract-algebra matrices eigenvalues-eigenvectors diagonalization
asked Nov 29 at 10:06
Nik
214
asked Nov 29 at 10:06
Nik
214
asked Nov 29 at 10:06
Nik
214
asked Nov 29 at 10:06
Nik
214
asked Nov 29 at 10:06
Nik
214
214
add a comment |
add a comment |
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