Linear Operators and Their Properties

Linear Operators and Their Properties

University

25 Qs

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Linear Operators and Their Properties

Linear Operators and Their Properties

Assessment

Quiz

Mathematics

University

Practice Problem

Hard

Created by

Deepa Balan

Used 1+ times

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25 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Let TT be a linear operator on an inner product space. TT is said to be normal if:

T=T∗T = T^*

T∗T=TT∗T^*T = TT^*

T∗=−TT^* = -T

TT is diagonalizable

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

If T is self-adjoint, then:

All eigenvalues of T are real

T is not normal

T has no eigenvalues

T is skew-symmetric

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following operators is always normal?

Self-adjoint operator

Skew-symmetric operator

Projection operator

Nilpotent operator

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

If T is a normal operator on a complex inner product space, then it is:

Not diagonalizable

Diagonalizable using an orthonormal basis

Diagonalizable only if it is unitary

Always self-adjoint

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The matrix of a self-adjoint operator is:

Skew-Hermitian

Unitary

Hermitian

Orthogonal

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The matrix of a unitary operator is:

Hermitian

Orthogonal

Normal

Skew-Hermitian

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following is not a property of a unitary operator?

Length-preserving

Angle-preserving

T∗T=IT^*T = I

T∗=−TT^* = -T

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