
Linear Operators and Their Properties
Quiz
•
Mathematics
•
University
•
Practice Problem
•
Hard
Deepa Balan
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25 questions
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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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