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What is the meaning of the multiplication of matrix B(composed of eigenvectors) and the transpose of B (eigenvectors are of a matrix A)? So, B's column vectors are eigenvectors of A, and I want to know what is the meaning of B*transpose(B)?

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    Can you clarify your question a bit? I find it hard to follow.2011-04-10
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    Hope I am clear enough now.2011-04-10
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    it's the matrix of the inner product in the basis given by the eigenvectors of $A$ - is it enough?2011-04-10
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    @baboon: Yes, it makes sense now.2011-04-10
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    @user8268: it is definitely inner product, but I'd like to know the properties of this matrix, I guess it is the projection matrix , it is orthogonal, and if I want to project a new sample vector to this matrix, so to do dimensionality reduction, correct me.2011-04-10
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    Do you really mean just any eigenvectors of $A$? Or do you mean linearly independent eigenvectors? Or do you mean an orthonormal basis consisting of eigenvectors of a symmetric/hermitian matrix $A$? (In that case $BB^T$ would be the identity.)2011-04-10
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    Yes, matrix A is symmetric, positive, semidefinite2011-04-10

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