/*! 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} Q31E Are the rows of an orthogonal ma... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q31E (page 233)

Are the rows of an orthogonal matrix A necessarily orthonormal?

Short Answer

Expert verified

Yes.

Step by step solution

01

Definition of an Orthonormal matrix.

In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors.

One way to express this is. Where QT is the transpose of Q and I is the identity matrix.

For example,

QTQq鈬赌1Tq鈬赌2Tq鈬赌3T..q鈬赌nTq鈬赌1,q鈬赌2,q鈬赌3,........q鈬赌n

02

According to above definition.

Let A be an orthogonal matrix. Let A=v鈬赌1....v鈬赌n.

Observe that for any v鈬赌鈭�Rn,

ATv鈬赌=AATv鈬赌=Iv鈬赌=v鈬赌

Hence, the row of an orthogonal matrix is orthonormal.

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

If A=QRis a QRfactorization, what is the relationship between ATA and RTR?

TRUE OR FALSE? The equation det(AT)=det(A)holds for all 2脳2matrices A.

If the nxnmatrices Aand Bare orthogonal, which of the matrices in Exercise 5 through 11 must be orthogonal as well? B-1AB.

Among all the vectors in Rnwhose components add up to 1, find the vector of minimal length. In the casen=2 , explain your solution geometrically.

Consider an invertible n脳nmatrix A. Can you write Aas A=LQ, where Lis a lowertriangular matrix andQis orthogonal? Hint: Consider the QRfactorizationof AT.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Mechanics Maths

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.