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Let V be the vector space of 2 × 2 matrices over R, let <A, B>=...

Let V be the vector space of 2 × 2 matrices over R, let <A, B>= tr(ABT ) be an inner product on V , and let U ⊆ V be the subspace of symmetric 2 × 2 matrices. Compute the orthogonal projection of the matrix A = (1 2

3 4)

on U, and compute the minimal distance between A and an element of U.

Hint: Use the basis 1 0 0 0  

0 0 0 1  

0 1 1 0 of U.

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