Find the singular values of the matrix.
-$$\left[ \begin{array} { r r }
- 8 & 0 \
0 & 6
\end{array} \right]$$
A) 8,6
B) 64,36
C) $- 8,6$
D) $- 64,36$

Question

Find the singular values of the matrix.
-$$\left[ \begin{array} { r r } 
- 8 & 0 \
0 & 6
\end{array} \right]$$
A) 8,6
B) 64,36
C) $- 8,6$
D) $- 64,36$

Quizplus · Accepted Answer

The singular values of a matrix are the square roots of the eigenvalues of $A^TA$, where $A$ is the given matrix. For the given matrix, $A^TA$ is a diagonal matrix with diagonal entries 64 and 36, so the singular values are the square roots of these, which are 8 and 6, respectively. Singular values are always non-negative.

Find the Singular Values of the Matrix [−8006]\left[ \begin{array} { r r } - 8 & 0 \\0 & 6\end{array} \right][−80​06​]

Find the Singular Values of the Matrix $\left[ \begin{array} { r r } - 8 & 0 \\0 & 6\end{array} \right]$