Question: Let the matrix A = (aij) represent a linear operator f with respect to the orthonormal basis x1; x2; . . . ; xn. Then

Let the matrix A = (aij) represent a linear operator f with respect to the orthonormal basis x1; x2; . . . ; xn. Then the sum
Let the matrix A = (aij) represent a linear operator

defines a quadratic form on X, where x1; x2; . . . ; xn are the coordinates of x relative to the basis.

i=1 j=1

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