What is Transition matrix: Definition and 64 Discussions

In control theory, the state-transition matrix is a matrix whose product with the state vector


{\displaystyle x}
at an initial time



{\displaystyle t_{0}}


{\displaystyle x}
at a later time


{\displaystyle t}
. The state-transition matrix can be used to obtain the general solution of linear dynamical systems.

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  1. A

    Engineering How do I find the transition matrix of this dynamic system?

    Hello! I have the following matrix (picture 1.)and I am susposed to find the transition matrix ($$ \phi $$) now for that I need the eigenvalue and vectors of this matrix A. The eigenvalues are 1,1 and 2. The eigenvectors I have found to be (1 0 0) (1 1 0) (5 3 1). Now to find the transition...
  2. WMDhamnekar

    A Coin flipping problem (Markov chain)

    b)Suppose that the coin flipped on Monday comes up heads. What is the probability that the coin flipped on Friday of the same week also comes up heads? My attempt to answer this question:
  3. C

    Transition matrix of a paint ball game

    Summary: Finding the transition matrix of a paint ball game where only 3 probabilities are given. We have the following question: Alice, Tom, and Chloe are competing in paint ball. Alice hits her target 40% of the time, Tom hits his target 25% of the time, and Chloe hits her target 30% of the...
  4. J

    The infinite limits of the probability transition matrix for Markov chain

    Consider a Markov chain with state space {1, 2, 3, 4} and transition matrix P given below: Now, I have already figured out the solutions for parts a,b and c. However, I don't know how to go about solving part d? I mean the question says we can't use higher powers of matrices to justify our...
  5. A

    A Question about a property of a matrix of transition probabilities

    In a 2012 article published in the Mathematical Gazette, in the game of golf hole score probability distributions were derived for a par three, four and five based on Hardy's ideas of how an hole score comes about. Hardy (1945) assumed that there are three types of strokes: a good (##G##)...
  6. S

    B Question about transition matrix of Markov chain

    The note I get from the teacher states that for transition matrix, the column part will be current state and the row part will be future state (let this be matrix A) so the sum of each column must be equal to 1. But I read from another source, the row part is the current state and the column...
  7. weningth

    A How to deal with colour indices on spinors

    I want to calculate transition amplitudes in QCD for processes like ##q(k)q^\prime(p)\rightarrow q(k^\prime)q^\prime(p^\prime)##, where ##q,q^\prime## are quarks. However, I am unsure what to do with the colour indices of the quark spinors upon squaring the matrix element. For the sake of...
  8. S

    MHB Markov chains- Can I have some help creating the transition matrix for this scenario?

    I just discovered this website and want to thank everyone who is willing to contribute some of their time to help me. I appreciate it more than you know First off, assume that state 1 is Chinese and that state 2 is Greek, and state 3 is Italian. A student never eats the same kind of food for 2...
  9. M

    MHB Solving Transition Matrix: Octopus Training

    Hey! :o An octopus is trained to chosose from two objects A and B always the object A. Repeated training shows the octopus both objects, if the octopus chooses object A, he will be rewarded. The octopus can be in 3 levels of training: Level 1: He can not remember which object was rewarded...
  10. SetepenSeth

    Transition Matrix of T

    Homework Statement Find the transition matrix ##P## of a transformation defined as ##T:ℝ_2→ℝ_3## ##T:\begin{bmatrix}a\\b\end{bmatrix} = \begin{bmatrix}a+2b\\-a\\b\end{bmatrix}## For basis ##B=\begin{bmatrix}1\\2\end{bmatrix},\begin{bmatrix}3\\-1\end{bmatrix}##...
  11. grquanti

    I Jump probability of a random walker

    Hello everybody. I have a Markowian homogeneous random walk. Given the transition matrix of the chain, I know that ##P[ X(t) = i | X(t-1) = j ] ≡ P_{j→i}=T_{ij}## where ##T## is the transition matrix and ##X(t)## is the position of the walker...
  12. M

    Transition Matrix for Finite State Random Walk

    Homework Statement Define a simple random walk Yn on a finite state space S = {0, 1, 2, . . . , N} to be a random process that • increases by 1, when possible, with probability p, • decreases by 1, when possible, with probability 1 − p, and • remains unchanged otherwise. (a) Specify the...
  13. M

    SIS epidemics transition matrix

    Homework Statement [/B] The population is 50 The diseases is known to follow SIS dynamics with the following probabilities The number of infected individuals increases with probability 0.1 and it decreases with probability 0.05 the probability that nothing happens is 0.85 a) what is the...
  14. L

    Finding the transition matrix

    Homework Statement Let ##B_1 = {\begin{bmatrix} 1 \\ 1 \\ 1\\ 0 \end{bmatrix}}, {\begin{bmatrix} 1 \\ 1 \\ 0\\ 0 \end{bmatrix}}, {\begin{bmatrix} 0 \\ 0 \\ 1\\ 1 \end{bmatrix}} ## and ##B_2 = {\begin{bmatrix} 1 \\ 1 \\ 1\\ 1 \end{bmatrix}}, {\begin{bmatrix} 1 \\ 1 \\ 1\\ -1 \end{bmatrix}}...
  15. U

    MHB Markov Chains - Finding a Transition Matrix for Probabilities

    Hi! I have a question regarding making the transition matrix for the corresponding probabilities. The main problem I feel I have here is figuring out how to represent the probabilities in the question in the transition matrix. Like if something is 7 times more likely than something else.. Any...
  16. R

    Finding transition matrix, no % probability given

    Homework Statement Consider a quantum mechanical system with three states. At each step a particular particle transitions from one state to a different state. Empirical data show that if the particle is in State 1, then it is 7 times more likely to go to State 2 at the next step than to State...
  17. Xico Sim

    I Transition matrix element and Isospin

    Hi, guys. A type of problem that often appears is to find the relation between cross sections of some processes. An example would be: $$\pi _{- }+ p \rightarrow K_0 + \Sigma_0$$ $$\pi _{- }+ p \rightarrow K_+ + \Sigma_-$$ $$\pi _{+}+ p \rightarrow K_+ + \Sigma_+$$ To do this, I argue that...
  18. E

    Bases and Coordinates: B1 and B2 for [R][/3] - Homework Statement

    Homework Statement Let B1={([u][/1]),([u][/2]),([u][/3])}={(1,1,1),(0,2,-1),(1,0,2)} and B2={([v][/1]),([v][/2]),([v][/3])}={(1,0,1),(1,-1,2),(0,2,1)} a) Show that B1 is a basis for [R][/3] b) Find the coordinates of w=(2,3,1) relative to B1 c)Given that B2 is a basis for [R[/3], find...
  19. F

    Find basis B given the transition matrix and B'

    Homework Statement The Matrix P = 1 0 3 1 1 0 0 3 1 is the transition matrix from what basis B to the basis B' = {(1,0,0),(1,1,0),(1,1,1) for R3? Homework Equations [v]B=P[v]B' The Attempt at a Solution I'm looking...
  20. M

    MHB Transition matrix question

    Not really sure how to get started on this one:Find the long-term proportions, a and b, of the two states, A and B, corresponding to the transition matrix T=|0.7 0.4| | 0.3 0.6| Note, the matric is a 2x2 matrix Thanks
  21. M

    MHB What is the long-term percentage of city dwellers?

    Hi, I am having trouble with the following question, I've answered part a but I am not sure about part b: Suppose each year 20% of people who live in the country move into the city, while 10% of the city people move into the country. a) If in 2015, 50% of the population live in the cities, what...
  22. J

    Find State Transition Matrix (time variant)

    Homework Statement find the state transition matrix of a time varying system where: dX/dt = A*X with A = [-1 , exp(-t - (t^2)/2) ; ; 0 , t] (Matlab format - sorry but its easier) Homework Equations How to go about solving such problems in a systematic way? The Attempt at a Solution...
  23. I

    Matrices: word problem, transition matrix

    Homework Statement Hello! Please, take a look at the problem described in the attached file. The question is: Explain why the transition matrix does what we want it to do.Homework Equations The Attempt at a Solution (sorry, I don't know yet how to type formulas) I don't quite understand this...
  24. L

    Linear Algebra Transition Matrix Proof

    Homework Statement Prove the following theorem: Suppose that B, C, and D are ordered bases for a nontrivial finite dimensional vector space V. let P be the transition matrix from B to C, and let Q be the transition matrix from C to D. Then QP is the transition matrix from B to D...
  25. C

    Finding Transition Matrix from Bases

    Homework Statement Let So = {v1,v2,v3,v4} be a basis of the vector space V. S= {u1,u2,u3,u4} is a set of vectors defined as follows: u1 = 80v1 + 106v2 + 120v3 +164v4 u2 = 80v1 + 146v2 + 136v3 + 91v4 u3 = 90v1 + 143v2 + 122v3 + 70v4 u4 = 80v1 + 56v2 + 80v3 + 48v4 Find the Transition...
  26. C

    Transition matrix between two bases?

    Homework Statement Let So = {v1,v2,v3,v4} be basis of vector space V. And S = {u1,u2,u3,u4} be set of vectors defined as follows: u1 = 20v1 + 46v2 + 116v3 + 170v4 u2 = 20v1 + 86v2 + 147v3 + 174v4 u3 = 30v1 + 89v2 + 59v3 + 81v4 u4 = 15v1 + 27v2 + 12v3 + 9v4 Find transition matrix A from...
  27. C

    Finding Transition Matrix

    Homework Statement let a= {a1, a2, a3, a4} and b={b1,...,b4} and r = {r1,...,r4} Also, b1 = 4a1 b2 = 8a1 + 7a2 b3 = 4a1 + 4a2 + 4a3 b4 = 9a1 + 5a2 + 8a3 + 5a4 and r1 = 3b4 r2= 4b3 + 6b4 r3 = 9b2 + 3b3 + 9b4 r4 = 6b1 + 5b2 + 3b3 + 5b4 Find transition matrix from basis a to...
  28. jegues

    State Transition Matrix, Determining States

    Homework Statement An LTI system is given in state-space form, \left( \begin{array}{cc} \dot{x_{1}} \\ \dot{x_{2}} \end{array} \right) = \left( \begin{array}{cc} -1 & 0.5 \\ 1 & 0 \end{array} \right) \left( \begin{array}{cc} x_{1} \\ x_{2} \end{array} \right) + \left( \begin{array}{cc} 0.5 \\...
  29. M

    Transition matrix -> change of basis.

    Homework Statement B = {b1, b2, b3} and C = {c1, c2, c3} are two basis's for R3 where the connection between the basis vectors are given by b1 = -c1 + 4c2, b2 = -c1 + c2 + c3, b3 = c2 - 2c3 a) decide the transformation matric from basis B to basis C. A vector x is given in...
  30. A

    Transition matrix and rational canonical form

    Homework Statement I want to find the transition matrix for the rational canonical form of the matrix A below. Homework Equations The Attempt at a Solution Let ##A## be the 3x3 matrix ##\begin{bmatrix} 3 & 4 & 0 \\-1 & -3 & -2 \\ 1 & 2 & 1 \end{bmatrix}## The...
  31. M

    Transition Matrix ( Markov Chain Monte Carlo)

    1. -Find a regular transition matrix that is not time reversible, i.e., doesn't satisfy the balance equations? 2.Pi,j=0≠Pj,ifor some i and j My understanding from Markov Chain Monte Carlo is that for the transition matrix to be regular the matrix has to have all positives entries and each row...
  32. K

    MHB Transition Matrix: Polynomial to Coordinate Form

    Hi guys, I'm having a little difficulty in converting a set of two bases into a transition matrix. My problem lies in the bases, because they are in polynomial form compared to your elementary coordinate form. How would I go about finding the transitional matrix for this example... Thanks in...
  33. L

    Transition Matrix and Ordered Bases

    Let B and C be ordered bases for ℝn. Let P be the matrix whose columns are the vectors in B and let Q be the matrix whose columns are the vectors in C. Prove that the transition matrix from B to C equals Q-1P. I am stuck. Here is what I have. I know that if B is the standard basis in ℝn...
  34. L

    Transition Matrix and Ordered Bases

    Homework Statement Let B and C be ordered bases for ℝn. Let P be the matrix whose columns are the vectors in B and let Q be the matrix whose columns are the vectors in C. Prove that the transition matrix from B to C equals Q-1P. Homework Equations An ordered basis for a vector space V is...
  35. T

    Finding a transition matrix

    Homework Statement Let B = {(1,1,1),(1,2,2),(2,3,4)} be an ordered basis of R3, and let B` be the standard basis of R3. Find the transition matrix from B to B` and use it to find the coordinates of (1,2,3)T with respect to B. Homework Equations The Attempt at a Solution Is it...
  36. P

    Transition matrix question.

    Hello, Homework Statement D:R3[x]->R3[x] is defined thus for any p(x)=(a0)+(a1)x+(a2)x2+(a3)x3: D(p(x)) = a1 + (2a2)x + (33)2 I am asked to find [D]B where B is the standard basis {1,x,x2,x3} I am then asked to find the transition matrix from B to C, where C={1,1+x,x+x2,x2+x3}. Based on these...
  37. A

    Solving Transition Matrix Homework Statement

    Homework Statement The problem is in the attachment, but I'll try and rewrite it... Suppose for a Markov Chain with two states, we get the following results. 1. If P0=[0 1] then P1=[.4 .6] 2. If P0=[4/11 7/11] then P0=P1=P2=...and so on. With this information, find the transition...
  38. P

    Find a transition matrix from bases?

    Homework Statement I have 2 bases, a = {1, x, x^2} and b = {-2 - 2x + 3x^2 , 1 + 2x - x^2 , -1 - x + 2x^2} of P2. Find the transition matrix Pab. How is this done?? Homework Equations Since this is Linear Algebra, there aren't really any relevant "Equations" as such. More logic...
  39. P

    Find a transition matrix from bases problem

    Homework Statement I have 2 bases, a = {1, x, x^2} and b = {-2 - 2x + 3x^2 , 1 + 2x - x^2 , -1 - x + 2x^2} of P2. Find the transition matrix Pab. How is this done??Homework Equations Since this is Linear Algebra, there aren't really any relevant "Equations" as such. More logic based...
  40. R

    Finding the transition matrix

    Homework Statement I'm enormously frustrated with these problems. I've been trying to figure out how to find out what the transition matrix between C and B is for about 2 hours and I still can't get it. I've watched 4 youtube videos and read two websites as well as the section in my...
  41. A

    How to solve the markov transition matrix

    Homework Statement I design a markov model to study the availability of a node which will not work unless the network work: I make the following matrix. In which (i,j) means i is node up /down and j is network up/down. R1,R2 means the repair rate for node and network. F1,F2 means the failure...
  42. H

    Transition matrix, Jacobian.

    Hi: I`m new here, can someone tell me which is the difference between the transition matrix and the Jacobian?, I did some exercises of the both topics, but How is it related? Thanks for the attention Sorry for my English writing, but English is not my native language.
  43. C

    Markov transition matrix in canonical form?

    As I understand, a Markov chain transition matrix rewritten in its canonical form is a large matrix that can be separated into quadrants: a zero matrix, an identity matrix, a transient to absorbing matrix, and a transient to transient matrix. The zero matrix and identity matrix parts are easy...
  44. D

    State transition matrix to change initial conditions.

    Hey folks, I have an orbit in the circular restricted three body problem with initial conditions [x(0), 0, z(0), 0, y'(0), 0] I'm following this paper http://adsabs.harvard.edu/full/1984CeMec..32...53H on how to correct these initial conditions given the state transition matrix at a...
  45. N

    Computing Floquet transition matrix

    hi , I need to create a program on mathématica 8 to study the stability of my system using Floquet transition matrix . to compute the Floquet transition matrix I made this program based on a fourth order Runge Kutta integration : X1[t_] = {x1[t], x2[t], x3[t], x4[t], x5[t], x6[t] ...
  46. C

    Stochastic Process - Creating a Probability Transition Matrix

    Homework Statement The total population size is N = 5, of which some are diseased and the rest are healthy. During any single period of time, two people are selected at random from the population and assumed to interact. The selection is such that an encounter between any pair of individuals...
  47. C

    Probability Transition Matrix and Markov Chains

    Homework Statement Given a Probability transition matrix, starting in X0= 1, determine the probability that the process never reaches state 2. Homework Equations The Attempt at a Solution State 2 is not an observing state, so I'm not sure how to find this probability. Any help...
  48. M

    State Transition Matrix Calculation Using MATLAB: 5x5 Matrix Solution

    Homework Statement I am trying to find the state transition matrix of a 5x5 matrix. Is there a way to use MATLAB in this problem ? Homework Equations \Phi = (T^-1) x e^(Dt) x T Where D is 5x5 matrix containing the eigenvalues in the main diagonal, rest of elements are zeros. T...
  49. T

    Transition Matrix of Correlations

    Homework Statement Hi all, I've the following problem: I've a series of correlations matrices, suppose 15x15 matrix of correlations between waves heights. Giving an historical series of correlation values, how can I determine a model to establish that the next correlation matrix has a...
  50. D

    Normal Markov Transition Matrix: Converging to Steady-State Vector

    If a Markov transition matrix's columns add up to 1, the matrix is a normal Markov transition matrix. Since it is normal, the Markov process must converge to a steady-state vector. Is this correct?