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Find an SVD of each matrix [Hint: In Exercise 11, one choice for $U$ is $\left[\begin{array}{rrr}{-1 / 3} & {2 / 3} & {2 / 3} \\ {2 / 3} & {-1 / 3} & {2 / 3} \\ {2 / 3} & {2 / 3} & {-1 / 3}\end{array}\right]$ In Exercise $12,$ one column of $U$ can be $\left[\begin{array}{c}{1 / \sqrt{6}} \\ {-2 / \sqrt{6}} \\ {1 / \sqrt{6}}\end{array}\right].$]$\left[\begin{array}{rr}{1} & {1} \\ {0} & {1} \\ {-1} & {1}\end{array}\right]$

$A=U \Sigma V^{T}=\left[\begin{array}{ccc}{1 / \sqrt{3}} & {1 / \sqrt{2}} & {1 / \sqrt{6}} \\ {1 / \sqrt{3}} & {0} & {-2 / \sqrt{6}} \\ {1 / \sqrt{3}} & {-1 / \sqrt{2}} & {1 / \sqrt{6}}\end{array}\right]\left[\begin{array}{cc}{\sqrt{3}} & {0} \\ {0} & {\sqrt{2}} \\ {0} & {0}\end{array}\right]\left[\begin{array}{ll}{0} & {1} \\ {1} & {0}\end{array}\right]$

Algebra

Chapter 7

Symmetric Matrices and Quadratic Forms

Section 4

The Singular Value Decomposition

Introduction to Matrices

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In mathematics, the absolu…

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Okay, So for this program, we can see the Laferrari Magics eight chest post tens A. So, in this case, this metrics will be 2003 Since this man tricks is already on Dagenham a diagonal matrix. So the dragon, very off this metrics were belonged. The wind caused with three in the Lambda two. It was due to greed. Able these lambda when Lambda to guarantee that Lambda y is greater recourse to love that you So the single a value for metrics There were basically my wine cost the root off three and the signature because to root of two and the ways. So once we have this singular, singular values in the singular value decomposition the metrics kept her sigma equals to root off three 00 through tough 200 Remember that this metric sick mom should be a three by two magics the same size as the original Matrix A. And we also need to figure out the Eigen values off this hs post time say so. A transposed a minus love no one. I equals two minus 1000 So we can choose the again value. I can vector to be 01 And for Lambda to a transpose times a mine Islam, that toe I close to 0001 and the weekends simply, I guess simply choose the Agon vector the to be on 10 So in the single value decomposition off metrics, day matrix of EU will be 0110 Now, for the last piece, we need to figure out the Matrix Q So you want you cost one over Sigma 18 times to be one by a simple calculation, we have won over route off 31 over. Route off 31 over. Route off three. This is our of your one. And for you to you will be one of a stigma to a V two. So we have one over route off to zero and the minus one. Over what off to? Since we only have two singular values. So we need to construct a your three by ourself. So you have three should be a normal vector, which perpendicular to both u one u two. So we can choose your three to be, um, one over route of sticks. Um, why Nowhere ser minus two over route off six and the one over it of six. Okay, so by this, by this choice off you want you to you three hour matrix year. We'll be love for Roy. Just put off this. You want you to your three as the as each column in you and the the singular value decomposition for matrix A We will be you times stick mark time severe transpose. Okay, so we just write off this metrics out again pants the Capital Sigma. So it's root off 300 root of 200 times. Um, the Matrix v 0110 since these symmetric matrix, So beaches posey coast Toby yourself. So this is the result for this question.

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