Can someone confirm or refute my thinking regarding the diagonalizability of an orthogonal matrix and whether it's symmetrical?(adsbygoogle = window.adsbygoogle || []).push({});

A = [b_{1}, b_{2}, ..., b_{n}] | H = Span {b_{1}, b_{2}, ..., b_{n}}. Based on the definition of the span, we can conclude that all of vectors within A are linearly independent. Furthermore, we can then conclude that Rank(A) = n.

If Rank(A) = n then none of the vectors in A can be made as a linear combination of the other n-1 vectors. Since A can be row-reduced to an identity matrix and the transpose of the identity matrix is itself. Can it be concluded that the original matrix A is also symmetrical (A^{T}= A)?

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# Symmetry of Orthogonally diagonalizable matrix

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