Quadratic Functions, Optimization, and Quadratic Forms
is a diagonal matrix with d j > 0, j =1,...,n. • f(x)=(x−a)TMTDM(x−a), where M is a non-singular matrix and D is as above. 3 Characteristics of Symmetric Matrices A matrix M is an orthonormal matrix if MT = M−1. Note that if M is orthonormal and y = Mx, then y 2 = yTy = xTMTMx= xTM−1Mx= xTx = x 2, and so y = x. Anumberγ ∈ is an ...
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