/*! 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} Q44E Show that every complex 2 脳 2 m... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Q44E (page 375)

Show that every complex 2 脳 2 matrix is similar to an upper triangular 2 脳 2 matrix. Can you generalize this result to square matrices of larger size? Hint: Argue by induction.

Short Answer

Expert verified

By induction,we can prove that the S鈭�1ASis an upper triangular(and in fact, a diagonal) matrix

Step by step solution

01

Step 1:Let v be an eigen vector of A, Now let

S=[vv鈯�]

Indeed,

S鈭�1AS=1鈭�v鈭�[鉄�Ax,x鉄�00Ax鈯�,x鈯�]

which is an upper triangular (and in fact, a diagonal) matrix.

Similar result works for any n脳n matrix A, that is, ifv1is an eigenvalue of A, we can let

A=[v1v2鈥�vn]

wherevi+1=vi鈯�,鈭赌i=1,鈥�,n鈭�1.

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

For each of the matrices in Exercises 1 through 13, find all real eigenvalues, with their algebraic multiplicities. Show your work. Do not use technology.

[010001100]

Consider the matrix A=|abba|where aand bare arbitrary constants. Find all eigenvalues of A.

find an eigenbasis for the given matrice and diagonalize:

A=114[123246369]

For each of the matrices in Exercises 1 through 13, find all real eigenvalues, with their algebraic multiplicities. Show your work. Do not use technology.

[04-14]

For each of the matrices in Exercises 1 through 13, find all real eigenvalues, with their algebraic multiplicities. Show your work. Do not use technology.

[1234]
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Statistics

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.