Test T for diagonalizability, and if T is diagonalizable, find a basis B for V such that [T]B is a diagonal matrix. V = M2x2 (R) & T is defined by T(A) = A^T (A transpose)
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That does NOT define a matrix. Do you mean "show that any matrix, A, such that $\displaystyle A= A^T$ is diagonalizable"? What is the definition of $\displaystyle A^T$?
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