Question:
Consider two matrices: \( P = \begin{bmatrix} 1 & 2 \\ 0 & 1 \end{bmatrix} \) and \( Q = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \). Which of the following statements is/are true?
Consider two matrices: \( P = \begin{bmatrix} 1 & 2 \\ 0 & 1 \end{bmatrix} \) and \( Q = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \). Which of the following statements is/are true?
Updated On: Jul 12, 2024
- P and Q have same set of eigenvalues
- eigenvalues P and Q commute with each other
- P and Q have different sets of linearly independent eigenvectors
- P is diagonalizable
Hide Solution
Verified By Collegedunia
The Correct Option is A, B, C
Solution and Explanation
The correct Answers are (A) :P and Q have same set of eigenvalues (B):eigenvalues P and Q commute with each other (C):P and Q have different sets of linearly independent eigenvectors
Was this answer helpful?
0
0
Top GATE PH Mathematical Physics Questions
- The solution of Laplace’s equation satisfies which condition?
- GATE PH - 2026
- Mathematical Physics
- Laplace transforms
- If \( F_1(Q, q) = Qq \) is the generating function of a canonical transformation from \((p, q)\) to \((P, Q)\), then which one of the following relations is correct?
- Given that \( A^\alpha \) and \( B_\beta \) (\(\alpha, \beta = 1, 2, 3, \ldots, n\)) are contravariant and covariant vectors, respectively, and by convention, any repeated indices are summed over. Which of the following expressions is/are tensors?
- The Fourier transform and its inverse transform are respectively defined as:\[ \tilde{f}(\omega) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{+\infty} f(x) e^{i \omega x} dx \]and\[ f(x) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{+\infty} \tilde{f}(\omega) e^{-i \omega x} d\omega \]Consider two functions \( f \) and \( g \). Another function \( f * g \) is defined as:\[ (f * g)(x) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{+\infty} f(y) g(x - y) dy \]Which of the following relation is/are true?Note: Tilde (~) denotes the Fourier transform.
- GATE PH - 2024
- Mathematical Physics
- Fourier Transform
- Consider a vector field \( \vec{F} = (2xz + 3y^2)\hat{y} + 4yz^2\hat{z} \). The closed path (\( \Gamma \): \( A \rightarrow B \rightarrow C \rightarrow D \rightarrow A \)) in the \( z = 0 \) plane is shown in the figure.
\( \oint_\Gamma \vec{F} \cdot d\vec{l} \) denotes the line integral of \( \vec{F} \) along the closed path \( \Gamma \). Which of the following options is/are true?
View More Questions
Top GATE PH Questions
- For a particle executing simple harmonic motion, the restoring force is proportional to:
- GATE PH - 2026
- Superconductivity
- The eigenvalues of the Hamiltonian operator represent the:
- GATE PH - 2026
- Mechanics
- The solution of Laplace’s equation satisfies which condition?
- GATE PH - 2026
- Laplace transforms
- Which of the following Maxwell’s equations represents Faraday’s law of electromagnetic induction?
- GATE PH - 2026
- Atomic Physics
- For an ideal gas undergoing an adiabatic process, which quantity remains constant?
- GATE PH - 2026
- Thermodynamics
View More Questions