Consider an n x n matrix M that is not symmetric, and define the function g(x) = x Mx from Rn to R. Is g necessarily a quadratic form? If so, find the matrix of g.

M303 Section 1.8 Notes- Introduction to Linear Maps/Transformations 9-19-16 If is × matrix, then for any vector ℝ , multiplication by produces new vector ℝ ; if we regard vectors in ℝ as inputs on which acts by multiplication to give output in ℝ , and we arrive at notion of a function Function/map :ℝ → ℝ - rule which assigns unique output ℝ to each input ℝ goes from domain ℝ to target ℝ o Image of under - output