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Question: how to tell Maple that matrix is symmetric with real entries

Question:how to tell Maple that matrix is symmetric with real entries

rwether 15 Maple
linearalgebra
June 30 2011
1

I was going to demonstrate the action of Maple for a symmetric 3 by 3 real matrix with 1, 2, and 3 distinct eigenvalues and got strange results.  It may be that I need to explicitly tell Maple that the matrix is symmetric and real. (How would I do this?)

For example, after   with(LinearAlgebra)    I put   tmat1:=Matrix(3,3,[1,2,3,2,4,5,3,5,6]), and get eigenvalues with small imaginary parts (!).   When I put   tmat2:=Matrix(3,3,[0,1,1,1,0,1,1,1,0]), I get real eigenvalues but eigenvectors (columns) which are not orthogonal.  On the other hand   tmat3:=Matrix(3,3,[2,0,0,0,2,0,0,0,2])  works just fine.

Sorry to have to ask about such a simple point, and I appreciate any help!

robert
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