Let V = M2 (R) with inner product (A, B) = tr(AB) (trace of A times...

     

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Let V = M2 (R) with inner product (A, B) = tr(AB) (trace of A times the transpose of B). (a) Compute the norm of 2 00 (b) Prove that the following are orthonormal: 00 0 210 (c) Let W be the vector space spanned by the matrices above. Com- pute the orthogonal projection of the matrix e12 onto W. Let V = M2 (R) with inner product (A, B) = tr(AB) (trace of A times the transpose of B). (a) Compute the norm of 2 00 (b) Prove that the following are orthonormal: 00 0 210 (c) Let W be the vector space spanned by the matrices above. Com- pute the orthogonal projection of the matrix e12 onto W.