![]() We assume that has this form throughout the rest of this article. īy permuting rows and columns in (1) we can arrange that It follows that if is an eigenvalue of then is also an eigenvalue and it has the same algebraic and geometric multiplicities as. Įquation (2) shows that is similar to the inverse of its transpose and hence (since every matrix is similar to its transpose) similar to its inverse. The Lorentz group, representing symmetries of the spacetime of special relativity, corresponds to matrices with. ![]() ![]() What are some examples of pseudo-orthogonal matrices? For and, is of the form Since is orthogonal, this equation implies that and hence that Furthermore, is clearly nonsingular and it satisfies It is easy to show that is also pseudo-orthogonal. A matrix satisfying (1) is also known as a -orthogonal matrix, where is another notation for a signature matrix.
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