Let vt,... , v be elements of a complex inner product space. Let K denote the corresponding

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Let vt,... , v" be elements of a complex inner product space. Let K denote the corresponding n x n Gram matrix, defined in the usual manner.
(a) Prove that A- is a Hermitian matrix, as defined in Exercise 3.6.49.
(b) Prove that K is positive semi-definite, meaning zT K z ≥ 0 for all z ∈ C".
(c) Prove that K is positive definite if and only ............ are linearly independent.
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Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

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