Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Stuck on your homework problem? This step-by-step video should help.

Try Numerade Free for 30 Days

Like

Report

Let $V$ be a vector space with a basis $\mathcal{B}=\left\{\mathbf{b}_{1}, \ldots, \mathbf{b}_{n}\right\} .$ Find the $\mathcal{B}$ -matrix for the identity transformation $I : V \rightarrow V$

$I_{n}$

Calculus 3

Chapter 5

Eigenvalues and Eigenvectors

Section 4

Eigenvectors and Linear Transformations

Vectors

Campbell University

Oregon State University

Harvey Mudd College

Idaho State University

Lectures

02:56

In mathematics, a vector (…

06:36

01:23

Let $\mathcal{B}=\left\{\m…

01:48

Let $\mathcal{D}=\left\{\m…

04:18

Find the change-of-basis m…

01:26

01:57

09:03

01:40

Let $S$ be the subspace of…

03:17

04:45

Determine a basis for the …

01:52

were given a vector space V with a basis be with basis vectors, be one through bien and were asked to find the bee matrix for the identity transformation I from B to itself. So we have the B coordinate vector of B J. Well, this is simply going to be e j, which is the standard basis vector for RN. This is because, for example, we have that P J is going to be zero times be one all the way up to zero times B J minus one plus one times B J plus zero times B J plus one all the way up to zero times bien. So it follows that thebe coordinate vector of the image of B. J. This is the same as Thebe. Coordinate Fechter of B J Since I is just the identity which we are too determined is E J and therefore the identity matrix relative to be This is going to the matrix with columns standard basis vectors e one e two through eat n. We see that this is the same as the identity matrix dimensions and by n

View More Answers From This Book

Find Another Textbook

In mathematics, a vector (from the Latin word "vehere" meaning &qu…

In mathematics, a vector (from the Latin "mover") is a geometric o…

Let $\mathcal{B}=\left\{\mathbf{b}_{1}, \mathbf{b}_{2}, \mathbf{b}_{3}\right…

Let $\mathcal{D}=\left\{\mathbf{d}_{1}, \mathbf{d}_{2}\right\}$ and $\mathca…

Find the change-of-basis matrix $P_{B} \leftarrow c$ from the given basis $C…

Find the change-of-basis matrix $P_{B \leftarrow C}$ from the given basis $C…

Find the change-of-basis matrix $P_{C \leftarrow B}$ from the given ordered …

Let $S$ be the subspace of $\mathbb{R}^{3}$ consisting of all vectors of the…

Determine a basis for the subspace of $M_{2}(\mathbb{R})$ spanned by $\left[…

Let $\mathcal{B}=\left\{\mathbf{b}_{1}, \ldots, \mathbf{b}_{n}\right\}$ be a…

01:47

In Exercises $9-16,$ find a basis for the eigenspace corresponding to each l…

02:58

Let $U$ and $V$ be $n \times n$ orthogonal matrices. Explain why $U V$ is an…

03:15

Is it possible that all solutions of a homogeneous system of ten linear equa…

05:10

Show that if $A^{2}$ is the zero matrix, then the only eigenvalue of $A$ is …

Determine which sets of vectors are orthogonal.$\left[\begin{array}{r}{1…

02:05

Let each matrix in Exercises $1-6$ act on $\mathbb{C}^{2} .$ Find the eigenv…

00:48

Exercises $7-12$ require MATLAB or other computational aid. In Exercises 7 a…

04:26

In Exercises $9-18$ , construct the general solution of $\mathbf{x}^{\prime}…

In Exercises 31 and $32,$ let $A$ be the matrix of the linear transformation…

04:38

In Exercises $25-28$ , show that the given signal is a solution of the diffe…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.