GATE DA concept:eigenvalues PYQs & Answers

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concept:eigenvalues

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Questions 1–5 of 5. Imported answers require independent review unless marked reviewed.

Topic practice 5 questionsPage 1 of 1

Let

be the eigenvalues of the matrix

where

is in radians.

Which one of the following options lists all the possible values of

satisfying

Your answerChoose one option.

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Let

be a system of orthonormal vectors in

. Consider the matrix

. Which of the following statements is/are correct?

Your answerSelect all correct options. You can choose more than one.

Singular values of

are also its eigenvalues

Singular values of

are either 0 or 1

Determinant of

is 1

is invertible

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matrix

with real entries satisfies the property:

, for all

, where

denotes the Euclidean norm. Which of the following statements is/are ALWAYS correct?

Your answerSelect all correct options. You can choose more than one.

must be orthogonal

, where

denotes the identity matrix, is the only solution

The eigenvalues of

are either

has full rank

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Let

be a dataset of

observations where each

. It is given that

. The covariance matrix computed from

has eigenvalues

. Let

be the direction of maximum variance with

The value of

(Answer in integer)

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Consider the matrix

Which ONE of the following statements is TRUE?

Your answerChoose one option.

The eigenvalues of

are non-negative and real.

The eigenvalues of

are complex conjugate pairs.

One eigenvalue of

is positive and real, and another eigenvalue of

is zero.

One eigenvalue of

is non-negative and real, and another eigenvalue of

is negative and real.

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GATE DA concept:eigenvalues PYQs

How to practice concept:eigenvalues

Question 46

Question 50

Question 52

Question 60

Question 13