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Linear Algebra and Learning from Data

Exercise 1.6.13

Answers

Any vector $x$ is a combination $x = c_{1} x_{1} + \dots + c_{n} x_{n}$ , then

$Ax = A (c_{1} x_{1} + \dots + c_{n} x_{n}) = c_{1} A x_{1} + \dots + c_{n} A x_{n} = c_{1} λ_{1} x_{1} + \dots + c_{n} λ_{n} x_{n}$
$Bx = B (c_{1} x_{1} + \dots + c_{n} x_{n}) = c_{1} B x_{1} + \dots + c_{n} B x_{n} = c_{1} λ_{1} x_{1} + \dots + c_{n} λ_{n} x_{n}$

So we have $Ax = Bx$ for any $x$ , take $x = 1$ , we have $A = B$ .

niuers

2020-03-20 00:00

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