I would like to know why the minimal polynomial of a graph $G$ is $m(x) = \prod(x-λ_i)$ where the product is taken over all distinct eigenvalues $λ_i$.
2026-03-25 06:08:16.1774418896
Minimal polynomial of a graph
356 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in ALGEBRAIC-GRAPH-THEORY
- Normalized Laplacian eigenvalues of a path graph
- Can i consider ($\emptyset, \infty, \emptyset$) to denote a null graph?
- number of edges in infinite graph
- 2-fold covers of graphs, their spectrum and the matching polynomial
- Is the following fact for laplace matrix true? And how to prove it?
- Automorphisms of cospectral k-regular graphs
- Understanding Generalised Quadrangles
- For any sets $X$ & $Y$ can the group of automorphisms for the digraph $G(X,Y)=(X\cup Y,X\times Y)$ be express in terms of symmetric groups?
- Proof that bipartite graph has perfect matching if and only if zero sub-matrix is not included
- Convergence of function with matrix as input
Related Questions in MINIMAL-POLYNOMIALS
- Minimal polynomial of $f(A) = A^t$
- Minimal polynomial of $ab$, when those of $a$ and $b$ are known
- Finding the minimal polynomial of $uv$, when those of $u$ and $v$ are given and of degree three
- Jordan chevaley decomposition and cyclic vectors
- A field extension of degree $\leq 2$
- For a non diagnolizable Matrix $A_{n\times n}$ exists a non zero polynomial $p(t)$ of degree $< n$ s.t. $(p(A))^2=0$
- minimal polynomial, $E_p=\cos\frac{2\pi}{p} + i\sin\frac{2\pi}{p}$
- Minimal polynomial of $\sqrt{3}$ over $\Bbb{Q}(\sqrt[6]{3})$
- Irreducibility of $f(x)=x^4+4x-1$
- Jordan forms associated with characteristic polynomials and minimal polynomials
Related Questions in ADJACENCY-MATRIX
- Shape of the graph spectrum
- Use the definition of matrix multiplication to explain why the analogous result holds for any entry of Adjacency Matrix $A^2$.
- Do isomorphic graphs have same values for adjacency matrices and spectrum?
- Edge-to-edge incidence structure of a graph
- Is there an approximation to a matrix $V = (I-cA)^{-1}$ where $I$ is the identity matrix and $A$ is an adjacency matrix of a connected graph?
- Is it possible to normalize a symmetric matrix without breaking symmetry?
- Spectral radius of a complete bipartite graph
- What is a suitable index to express similarity in two observations of the same set of variables containing ratios?
- How to find Eulerian path in the given graph?
- Spectral radius of a complete tripartite graph
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?
That's because the adjacency matrix of an undirected graph is symmetric, thus diagonalizable. That means that every irreducible factor of minimal polynomial has multiplicity one.