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Topic: Principal Vectors
Replies: 5   Last Post: Sep 25, 2011 10:25 PM

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Worawut Wisutmethangoon

Posts: 6
Registered: 12/12/04
Principal Vectors
Posted: Jun 9, 1997 6:57 AM
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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.





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