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Exercise 1.7.4

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In the false proof, we have $λ = \frac{x^{T} Ax}{x^{T} x}$ . However, it’s possible that $x^{T} x$ can be zero when $x \neq 0$ , for example, if $x = (i, 1)$ , then we have $x^{x} = 0$ . When this is true, we can’t use the formula to solve for $λ$ . On the other hand, if we use conjugate of $x$ , i.e. ${\bar{x}}^{T} x$ , we only get zero when $x = 0$ , so for any nonzero $x$ , we have ${\bar{x}}^{T} x > 0$ , this is not true for $x^{T} x$ .

niuers

2020-03-20 00:00

Exercise 1.7.4

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