1.6 Orthogonal Matrices

The following properties hold for orthogonal matrices \(A_{n\times n}\)

1.

\(\displaystyle {A^{-1} = A'}\)

2.

\(\displaystyle {A'A = I}\)

3.

\(\displaystyle { \begin {vmatrix} A\\ \end {vmatrix} = \pm 1 }\)

4.

\(\displaystyle { \underline {\theta }'_i\underline {\theta }_j = \begin {cases} 1, & i=j\\ 0, & i\neq j \end {cases} }\)

5.

\(C=AB\) is orthogonal if \(A\) and \(B\) are orthogonal.

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