Prove that Markov chain will be irreducible if its transition matrix is doubly stochastic.
I was told to use Birkhoff's theorem, but I don't know how to use it at all.
2026-02-24 06:45:15.1771915515
Doubly stochastic matrix
222 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in MATRICES
- How to prove the following equality with matrix norm?
- I don't understand this $\left(\left[T\right]^B_C\right)^{-1}=\left[T^{-1}\right]^C_B$
- Powers of a simple matrix and Catalan numbers
- Gradient of Cost Function To Find Matrix Factorization
- Particular commutator matrix is strictly lower triangular, or at least annihilates last base vector
- Inverse of a triangular-by-block $3 \times 3$ matrix
- Form square matrix out of a non square matrix to calculate determinant
- Extending a linear action to monomials of higher degree
- Eiegenspectrum on subtracting a diagonal matrix
- For a $G$ a finite subgroup of $\mathbb{GL}_2(\mathbb{R})$ of rank $3$, show that $f^2 = \textrm{Id}$ for all $f \in G$
Related Questions in MARKOV-CHAINS
- Calculating probabilities using Markov chains.
- Probability being in the same state
- Random walk on $\mathbb{Z}^2$
- Polya's Urn and Conditional Independence
- Markov Chain never reaches a state
- Finding a mixture of 1st and 0'th order Markov models that is closest to an empirical distribution
- Find probability function of random walk, stochastic processes
- Generating cycles on a strongly connected graph
- Will be this random walk a Markov chain?
- An irreducible Markov chain cannot have an absorbing state
Related Questions in TRANSITION-MATRIX
- Transition probabilities for many-states Markov model
- Markov Chain - find missing transition values
- Find the transition matrix $P_{S\leftarrow T}$
- A vector $\mathbf{x}\in X$ has coordinates $\mathbf{x}_\mathcal{B}= \langle2,-7,-10\rangle$. What is $\mathbf{x}_\mathcal{G}$?
- A vector $x∈X$ has coordinates $x_B=⟨2,−7,−10⟩$. What is $x_J$?
- transition rates from transition probabilities
- Trying to grasp how to compute a $n$-step transition probability
- Change of Basis Given 2 Vectors and Transition Matrix
- What is the difference between a transition function and a transition kernel?
- Markov chain constant transition matrix
Related Questions in STOCHASTIC-MATRICES
- Stochastic matrix question
- Limiting state vector of a $3$-state Markov chain
- Proving or disproving product of two stochastic matrices is stochastic
- Proving product of two column stochastic matrices is column stochastic (Proof verification)
- Decompose stochastic matrix in product of two stochastic matrices
- Examples of stochastic matrices that are also unitary?
- Cesàro limit of a stochastic matrix
- Is the Birkhoff–von Neumann theorem true for infinite matrices?
- Maximum column sum of stochastic matrix
- Prove that : There exists a vector $x$ such that $Mx = x$ , where $M$ is a Markov matrix
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?