Let T be defined by a) Show that the and that the eigenvalues are given by 1 and -1 b) Determi...

Question

Question

Let T be defined by

$T(x_1,x_2,x_3, x_4,\dots) = (x_1,-x_2,x_3,-x_4,\dots)$

a) Show that the $TEB$ and that the eigenvalues are given by 1 and -1

b) Determine the eigenvectors

TEB

math Advanced-Math

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

0 80 (1) T (o, -1 0 2 5 I, o 0 2

Add a comment

Answer 2

Similar Homework Help Questions

1. Let and . Find the eigenvalues of this matrix and determine if it is invertible. In other wo...

1. Let and . Find the eigenvalues of this matrix and determine if it is invertible. In other words, how does finding a basis of for which the matrix of is upper triangular help find the eigenvalues of and how does it help determine is is invertible? 2. Define by . Find all the eigenvalues and eigenvectors of . Note stands for either or . TE L(V) 0 0 8 We were unable to transcribe this imageWe were unable to...
Let be a topological space, let and be paths in such that . Show that defined...

Let be a topological space, let and be paths in such that . Show that defined by is a path in We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Let V be a Hilbert space. Let S1 and S2 be two hyperplanes in V defined by Let be given. We con...

Let V be a Hilbert space. Let S1 and S2 be two hyperplanes in V defined by Let be given. We consider the projection of y onto , i.e., the solution of (1) (a) Prove that is a plane, i.e., if , then for any . (b) Prove that z is a solution of (1) if and only if and (2) (c) Find an explicit solution of (1). ( d) Prove the solution found in part (c) is unique. We...

Apply the operator as defined in equation 4.129, and the operator as defined in equation 4.132...

Apply the operator as defined in equation 4.129, and the operator as defined in equation 4.132 to the hydrogen state to show that they have the eigenvalues given in equation 4.133. [4.129] We were unable to transcribe this image[4.133] We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Let two variables and are bivariately normally distributed with mean vector component and and co-variance matrix...

Let two variables and are bivariately normally distributed with mean vector component and and co-variance matrix shown below: . (a) What is the probability distribution function of joint Gaussian ? (Show it with and ) (b) What is the eigenvalues of co-variance matrix ? (c) Given the condition that the sum of squared values of each eigenvector are equal to 1, what is the eigenvectors of co-variance matrix ? please help with all parts! thank you! X1 We were unable...
1. Let be the operator on whose matrix with respect to the standard basis is . a) Verify the result of proof " is normal if and only if for all " for question 1. Note: stands for adjoint...

1. Let be the operator on whose matrix with respect to the standard basis is . a) Verify the result of proof " is normal if and only if for all " for question 1. Note: stands for adjoint b) Verify the result of proof "Orthogonal eigenvectors for normal operators" for question 1. The proof states suppose is normal then eigenvectors of corresponding to distinct eigenvalues are orthogonal. We were unable to transcribe this imageWe were unable to transcribe this...

Let a,b and c be real numbers and consider the function defined by . For which values of a,b,...

Let a,b and c be real numbers and consider the function defined by . For which values of a,b, and c is f one-to-one and or onto ? Show all work. f:R→R We were unable to transcribe this imageWe were unable to transcribe this image f:R→R
Let T: be defined as . Prove or disprove that can be written as the sum of two one-dimensional, T-invariant subspace...

Let T: be defined as . Prove or disprove that can be written as the sum of two one-dimensional, T-invariant subspaces. IR IR We were unable to transcribe this imageWe were unable to transcribe this image IR IR
Let a and be be in . Show the following. If gcd(a,b)=1, then for every n...

Let a and be be in . Show the following. If gcd(a,b)=1, then for every n in there exist x and y in such that n=ax+by. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image

Let T : C([0, 1]) → R be a (not necessarily bounded) linear functional. Show that...

Let T : C([0, 1]) → R be a (not necessarily bounded) linear functional. Show that T is positive if and only if = (here 1 denotes the constant function [0, 1] → R, x → 1). We were unable to transcribe this imageWe were unable to transcribe this image

Let T be defined by a) Show that the and that the eigenvalues are given by 1 and -1 b) Determi...

Homework Answers

Add Answer to:
Let T be defined by a) Show that the and that the eigenvalues are given by 1 and -1 b) Determi...

Post as a guest

Earn Coins

1. Let and . Find the eigenvalues of this matrix and determine if it is invertible. In other wo...

Let be a topological space, let and be paths in such that . Show that defined...

Let V be a Hilbert space. Let S1 and S2 be two hyperplanes in V defined by Let be given. We con...

Apply the operator as defined in equation 4.129, and the operator as defined in equation 4.132...

Let two variables and are bivariately normally distributed with mean vector component and and co-variance matrix...

1. Let be the operator on whose matrix with respect to the standard basis is . a) Verify the result of proof " is normal if and only if for all " for question 1. Note: stands for adjoint...

Let a,b and c be real numbers and consider the function defined by . For which values of a,b,...

Let T: be defined as . Prove or disprove that can be written as the sum of two one-dimensional, T-invariant subspace...

Let a and be be in . Show the following. If gcd(a,b)=1, then for every n...

Let T : C([0, 1]) → R be a (not necessarily bounded) linear functional. Show that...

Let T be defined by a) Show that the and that the eigenvalues are given by 1 and -1 b) Determi...

Homework Answers

Add Answer to: Let T be defined by a) Show that the and that the eigenvalues are given by 1 and -1 b) Determi...

Post as a guest

Earn Coins

Add Answer to:
Let T be defined by a) Show that the and that the eigenvalues are given by 1 and -1 b) Determi...