Suppose T 2 L.V / and T has a block diagonal matrix0B@A1 0:::0 Am1CAwith respect to some
Chapter 9, Problem 7(choose chapter or problem)
Suppose T 2 L.V / and T has a block diagonal matrix0B@A1 0:::0 Am1CAwith respect to some basis of V. For j D 1; : : : ; m, let Tj be the operatoron V whose matrix with respect to the same basis is a block diagonalmatrix with blocks the same size as in the matrix above, with Aj in thej th block, and with all the other blocks on the diagonal equal to identitymatrices (of the appropriate size). Prove that T D T1 Tm.
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