Cn Ahxee
(ie replace all the T with ) Hence, we get the following result Prop is an inner product on Cn if and only if = xAy, where Ais a selfadjoint matrix whose eigenvalues are strictly positive 4.
Cn ahxee. An(x−c)n = x−c lim n→∞ an1 an By the ratio test, the power series converges if 0 ≤ r. 3 Inner products on Cn In fact, a similar proof works for Cn, except that you have to replace all the transposes by adjoints!.
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