GATE PH concept:matrices PYQs & Answers

Questions 1–3 of 3. Imported answers require independent review unless marked reviewed.

Consider two matrices:

and

. Which of the following statement is/are true?

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

P and Q have same set of eigenvalues

P and Q commute with each other

P and Q have different sets of linearly independent eigenvectors

P is diagonalizable

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Consider a two dimensional Cartesian coordinate system in which a rank 2 contravariant tensor is represented by the matrix

. The coordinate system is rotated anticlockwise by an acute angle

with the origin fixed. Which one of the following matrices represents the tensor in the new coordinate system?

Your answerChoose one option.

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and

are two Hermitian matrices and there exists a matrix

, which diagonalizes both of them, such that

and

, where

and

are diagonal matrices. The correct statement(s) is(are)

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

All the elements of both matrices

and

are real.

The matrix

can have complex eigenvalues.

The matrix

can have complex eigenvalues.

The matrices

and

commute.

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GATE PH concept:matrices PYQs