A matrix P \in \mathbb {R}^{d \times d} is orthogonal (sometimes referred to as a rotation matrix ) if P P^ T = P^ T P = I_ d. Suppose that

Question

P = \begin{pmatrix} v_1 & v_2 & \cdots & v_ d \\ \end{pmatrix}

where v_1, v_2, \ldots , v_ d \in \mathbb {R}^ d are column vectors.

Is the identity matrix I_ d an orthogonal matrix?

Yes

No
unanswered
What is \sum _{i = 1}^ d (v_1^ i)^2?

unanswered
What is v_1 \cdot v_2?

unanswered
Are the rows of P unit vectors?

Yes

No

Answer 1

Yes