/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q8E The singular values of any matri... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Q8E (page 413)

The singular values of any matrix Aare the eigenvalues of matrixATA.

Short Answer

Expert verified

The given statement is FALSE.

Step by step solution

01

Step 1: Definition of singular values:

The diagonal entries of the matrix are singular values, which are arranged in ascending order.

The singular values are found from the non- zero eigenvalues ofATA.

Hence, singular value is 蟽=位.

02

Step 2: To Find TRUE or FALSE

The singular values ofA are the square roots of the eigenvalues of ATA.

Considerrole="math" localid="1664185016615" A=100-1

FindATas follows:

AT=100-1ATA=100-1100-1ATA=1001

Determine the singular values:

ATA-位I=01001-位00位=1-位001-位

Simplify further,

1-位1-位=0位=1

Hence, singular value is 蟽=位=1.

The singular values of A are, 1.

Hence, the given statement is FALSE.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Let 位 be a real eigenvalue of an n x n matrix A. Show that

蟽n猢�|位|猢�蟽1,

where蟽1and蟽nare the largest and the smallest singular values of A, respectively.

If A is an invertible 2x2matrix, what is the relationship between the singular values of A and A-1? Justify your answer in terms of the image of the unit circle.

54. If Aand B are real symmetric matrices such that,A3=B3 thenmust be equal to B.

If Ais an indefiniten脳n matrix, andR is a realn脳mrankn what can you say about the definiteness of the matrixRTAR?

IfA is any symmetric2脳2matrix with eigenvalues -2 and 3, andu鈫�is a unit vector in鈩�2,鈩�2, what are the possible values of||Au炉||? Explain your answer geometrically, using Example 4as a guide.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.