Proofs Homework Set 5
... are upper triangular. Proof. The elementary matrix corresponding to scaling, say, the ith row by k is the matrix with ones on the diagonal, except in the ith row, which instead has a k, and zeros everywhere else. In particuar, then, the (i, j)-th entry is zero when i > j. Next consider a replacemen ...
... are upper triangular. Proof. The elementary matrix corresponding to scaling, say, the ith row by k is the matrix with ones on the diagonal, except in the ith row, which instead has a k, and zeros everywhere else. In particuar, then, the (i, j)-th entry is zero when i > j. Next consider a replacemen ...
univariate case
... Theorem 12. Consider the set Pn of nonnegative univariate polynomials of degree less than or equal to n (n is even). Then, identifying a polynomial with its n + 1 coefficients (pn , . . . , p0 ), the set Pn is a proper cone (i.e., closed, convex, pointed, solid) in Rn+1 . An equivalent condition for t ...
... Theorem 12. Consider the set Pn of nonnegative univariate polynomials of degree less than or equal to n (n is even). Then, identifying a polynomial with its n + 1 coefficients (pn , . . . , p0 ), the set Pn is a proper cone (i.e., closed, convex, pointed, solid) in Rn+1 . An equivalent condition for t ...
