Question

Let K = C^{−1}AB. Suppose *v* is an eigenvector
of K. Find one eigenvector of A and the related eigenvalue.

Answer #1

**ANSWER :**

Given the data following that is if an V an eigen vector of C corresponding to the eigen value can ve determine that the corresponding to .

V is an eigen vector of A corresponding to .

By defination :

V is an eigen vector of B corresponding to Y.

By defination :

We have

Multiply both sides with A

By defination of eigen vector of AB M is an eigen value of AB. V is corresponding eigen vector .

v is an eigenvector with eigenvalue 5 for the invertible matrix
A. Is v an eigenvector for A^-2? Show why/why not.

Let A be an n × n matrix and let x be an eigenvector of A
corresponding to the eigenvalue λ . Show that for any positive
integer m, x is an eigenvector of Am corresponding to the
eigenvalue λ m .

Let (V, C) be a finite-dimensional complex inner product
space.
We recall that a map T : V → V is said to be normal if
T∗ ◦ T = T ◦ T∗ .
1. Show that if T is normal, then |T∗(v)| = |T(v)|
for all vectors v ∈ V.
2. Let T be normal. Show that if v is an eigenvector of T
relative to the eigenvalue λ, then it is also an eigenvector of
T∗ relative to...

Suppose A is a diagonalisable matrix and let k ≥ 1 be an
integer. Show that each eigenvector of A is an eigenvector of
Ak and conclude that Ak is diagonalisable

Suppose that the two operators A and B satisfy the commutation
relation [A, B] = B. Let |a > is an eigenvector
of A with an eigenvalue a, i.e. A|a >= a|a >. Show that
vector B|a > is also an eigenvector of A, and find the
corresponding eigenvalue.

Complete all of the exercises as soon as possible:
1. Find all k for which E = (k 1 k, 0 2 k, 0 1 3k) is
invertible.
2. Let A = (2 -1 0 3) and x = (1 -1).
You are given that x is an eigenvector of
A. What is the corresponding eigenvalue?

Verify that u=[1,13]T is an eigenvector of the matrix
[[ -8,1],[-13,6]]. Find the corresponding eigenvalue lambda.

Given Eigenvalue 3, -2. Respective Eigenvector V1 = [1 1], V2=
[1 -1]. Find the matrix A

1. Assume that V is a vector space and L is a linear function V
→ V.
a. Suppose there are two vectors v and w in V such that v, w,
and v+w are all eigenvectors of L. Show that v and w share the same
eigenvalue.
b. Suppose that every vector in V is an eigenvector of L. Prove
that there is a scalar α such that L = αI.

find the eigenvalues of the following matrix. then find the
corresponding eigenvector(s) of one ofthose eigenvalues (pick your
favorite).
1 -2 0
-1 1 -1
0 -2 1

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 5 minutes ago

asked 5 minutes ago

asked 11 minutes ago

asked 11 minutes ago

asked 17 minutes ago

asked 45 minutes ago

asked 57 minutes ago

asked 57 minutes ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago