Orthogonal Matrices

Practice Questions

Linear Algebra › Orthogonal Matrices

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$\begin{align*}&\text{Conclude whether or not the matrix }A=\begin{bmatrix}-0.60587&0.79556\0.79556&0.60587\end{bmatrix}\&\text{is orthogonal.}\end{align*}$

Assume M is an orthogonal matrix. Which of the following is not always true?

is an unitary matrix.

True or false: $A^{2}$ must be an unitary matrix.

$A = \begin{bmatrix} 0 & 0 & i \ 0 &1 & 0 \- i & 0 & 0 \end{bmatrix}$

True or false: is an example of a unitary matrix.

$A = \begin{bmatrix} \frac{3}{5} & \frac{12}{25} & \frac{16 }{25} \ \ -\frac{4}{5} & \frac{9}{25} & \frac{12}{25} \ \ 0 & - \frac{4}{5} & \frac{3}{5} \end{bmatrix}$

True or false: is an example of an orthogonal matrix.

$\begin{align*}&\text{Conclude whether or not the matrix }A=\begin{bmatrix}0.68567&0.12975&-0.71626\0.14807&0.93855&0.31176\0.71269&-0.31982&0.62433\end{bmatrix}\&\text{is orthogonal.}\end{align*}$