Math Solutions

Solution: Let A=[cc-3 1 , 4 -1], B=[cc5 -2 , 2 1] ∈ R_2 * 2 under the inner product < A, B>=tr;(A^T B) where tr represents the sum of the diagonal

Question: Let $A=\left[\begin{array}{cc}-3 & 1 \\ 4 & -1\end{array}\right], B=\left[\begin{array}{cc}5 & -2 \\ 2 & 1\end{array}\right] \in \mathbb{R}_{2 \times 2}$ under the inner product $\langle A, B\rangle=\operatorname{tr}\left(A^{T} B\right)$ where tr represents the sum of

the diagonal entries of a matrix. Find the following.

$\langle A, B\rangle$
$\|B\|$
$d(A, B)$

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Solution: Let A=[cc-3 1 , 4 -1], B=[cc5 -2 , 2 1] ∈ R_2 * 2 under the inner product < A, B>=tr;(A^T B) where tr represents the sum of the diagonal

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