Let $A$ be a diagonalizable matrix, and $P$ be permutation matrix of same size. Does $A$ and $PAP$ have the same eigenvalues (or characteristic polynomial)?
2026-03-26 14:26:35.1774535195
Eigenvalues after multiplication with permutation matrix.
142 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in LINEAR-ALGEBRA
- An underdetermined system derived for rotated coordinate system
- How to prove the following equality with matrix norm?
- Alternate basis for a subspace of $\mathcal P_3(\mathbb R)$?
- Why the derivative of $T(\gamma(s))$ is $T$ if this composition is not a linear transformation?
- Why is necessary ask $F$ to be infinite in order to obtain: $ f(v)=0$ for all $ f\in V^* \implies v=0 $
- I don't understand this $\left(\left[T\right]^B_C\right)^{-1}=\left[T^{-1}\right]^C_B$
- Summation in subsets
- $C=AB-BA$. If $CA=AC$, then $C$ is not invertible.
- Basis of span in $R^4$
- Prove if A is regular skew symmetric, I+A is regular (with obstacles)
Related Questions in EIGENVALUES-EIGENVECTORS
- Stability of system of parameters $\kappa, \lambda$ when there is a zero eigenvalue
- Stability of stationary point $O(0,0)$ when eigenvalues are zero
- Show that this matrix is positive definite
- Is $A$ satisfying ${A^2} = - I$ similar to $\left[ {\begin{smallmatrix} 0&I \\ { - I}&0 \end{smallmatrix}} \right]$?
- Determining a $4\times4$ matrix knowing $3$ of its $4$ eigenvectors and eigenvalues
- Question on designing a state observer for discrete time system
- Evaluating a cubic at a matrix only knowing only the eigenvalues
- Eigenvalues of $A=vv^T$
- A minimal eigenvalue inequality for Positive Definite Matrix
- Construct real matrix for given complex eigenvalues and given complex eigenvectors where algebraic multiplicity < geometric multiplicity
Related Questions in CHARACTERISTIC-POLYNOMIAL
- How to determine the characteristic polynomial of the $4\times4$ real matrix of ones?
- Find eigenvalues given the characteristic polynomial without finding the roots
- Factorizing a polynomial.
- Find the characteristic polynomial |$\lambda - AI $| for this $5 \times 5$ matrix
- On the relation between traces and characteristic polynomials
- Question involving characteristic polynomial of a linear transformation
- How to compute the characteristic polynomial of a companion matrix to a polynomial with matrix-valued coefficients?
- Let $A$ be a $3\times 3$ matrix with characteristic polynomial $x^3-3x+a$, for what values of $a$ given matrix must be diagonalizable.
- Let $A$ be an $n \times n$ real matrix with $n \geq 2$ and characteristic polynomial $x^{n-2}(x^2-1)$, then
- Is $A$ the $2 × 2$ identity matrix?
Related Questions in PERMUTATION-MATRICES
- Storing permutation matrix in a vector form
- Prove that the determinant of a swap matrix is $-1$
- How to find a $3\times 3$ permutation matrix?
- Can you completely permute the elements of a matrix by applying permutation matrices?
- Finding eigenvalues and there properties of permutation matrix
- How do you find all solutions to the matrix equation $XAX=A^T$?
- Project an orthogonal matrix onto the Birkhoff Polytope
- Nearest signed permutation matrix to a given matrix $A$
- Permutation and permutation matrices
- Diagonalize the cyclic shift operator
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Since $P^\top = P^{-1}$ (it is not the case that $P = P^{-1}$), it follows that the matrices $A$ and $P^\top A P$ have the same characteristic polynomial and hence eigenvalues (the latter is called a permutation similarity).