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please help if you know Optimization with Quadratic Functions

Quadratic Functions A quadratic function is a mapping Q R R that is a scalar combination of single variables and pairs of var

Given an n × n matrix C, a text problem on p.5 shows that there is a matrix F such that F = FT and XT . C . X = X7, F. X for

Could you please prove 89.
Thank you so much !

Quadratic Functions A quadratic function is a mapping Q R R that is a scalar combination of single variables and pairs of variables. Thus, there are coefficients Cli,] and Ell, and a real number q, such that for X E IRn, we have The m atrix notation for C is suggestive. Indeed, C is n × n, and we take E to be 1 x n and then we see that
Given an n × n matrix C, a text problem on p.5 shows that there is a matrix F such that F = FT and XT . C . X = X7, F. X for all X E Rn Recall that a matrix that is equal to its transpose is called symmetric. Problem 89 Let A and B be n X n and symmetric, and suppose that v A .B.U for all v R". Show that A B. (Hint: let e, be the j-th column of the identity matrix in, and use u = ej and u-ej + ek.)
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