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Principal Vectors
Posted:
Jun 9, 1997 6:57 AM


Hello, I have a question hopefully any of you can help.
As you all know :
If we have a square matrix A, we can always find another square matrix X such that
X(1) * A * X = J where J is the matrix with Jordan canonical form. Column vectors of X are called principal vectors of A.
(If J is a diagonal matrix, then the diagonal members are the eigenvalues and column vectors of X are eigenvectors.)
It is also known that if A is real and symmetric matrix, then we can find X such that X is "orthogonal" and J is diagonal.
The question :
Are there any less strict conditions of A so that we can guarantee X orthogonal, with J not necessarily a diagonal ?
I would appreciate any answers and/or pointers to any references.
Thanks, Worawut W.



