Question 7.E.3.10: Show that e^A is an orthogonal matrix whenever A is skew sym......

Matrix Analysis and Applied Linear Algebra [1113429]

Show that $e^A$ is an orthogonal matrix whenever A is skew symmetric.

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The infinite series representation of $e^A$ shows that if A is skew symmetric, then $(e^A)^T = e^{A^{T}} = e^{−A},$ and hence $e^A (e^A)^T = e^{A−A} = e^0 = I.$

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