S . K . Sen, On computing an equivalent symmetric matrix for a nonsymmetric matrix, Intern.
32.
If is a real matrix, this is equivalent to ( that is, is a symmetric matrix ).
33.
The finite-dimensional spectral theorem says that any symmetric matrix whose entries are diagonalized by an orthogonal matrix.
34.
Sometimes the notation " J " is used instead of ? for the skew-symmetric matrix.
35.
All main diagonal entries of a skew-symmetric matrix must be zero, so the trace is zero.
36.
It's a symmetric matrix because the order in which you take partial derivatives doesn't matter.
37.
This equation can be written in matrix notation, in terms of a symmetric matrix to simplify some subsequent formulae, as
38.
Similarly, each diagonal element of a skew-symmetric matrix must be zero, since each is its own negative.
39.
Another concrete realization would be obtained by thinking of as the 3 & times; 3 symmetric matrix which represents it.
40.
A symmetric matrix and another symmetric and positive-definite matrix can be simultaneously diagonalized, although not necessarily via a similarity transformation.
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