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trapz.m function integrates along one dimension only. If one of them is $1$, then the nullspace of your system will be the space spanned by the eigenvectors associated with the eigenvalue $\lambda = 1$. It is N by M matrix of scalar values and I need to take 2D integral along both dimensions. These are the values of $\lambda$ that satisfy the right-hand eigenvalues equations above. Since you have access to a symbolic manipulation package, ask it to calculate the eigenvalues of $P^T$. If you want to do it by hand, search for "characteristic equation eigenvalues".
#Matlab symbolic toolbox matrices how to
This is a special case of the left-hand eigenvalue problem $xP = \lambda x$, or equivalently the transpose of the right hand nullspace of $P^T$, $P^T x^T = \lambda x^T$, with $\lambda = 1$.Įigenvalue problems are the subject of a great deal of study, and there are plenty of good explanations already available on how to solve them. cell arrays and structures, and the Symbolic Mathematics toolbox. Since you're looking for the transpose of the nullspace of $(P - I)^T$, this is equivalent to solving the equation $(P - I)^Tx^T = 0$, which, after rearrangement, is equivalent to $xP = x$. 2D Discrete wavelet transform in matlab Feature extraction of image using wavelet. The nullspace of a matrix $A$ is, by definition, the set of all vectors $x$ such that $Ax = 0$.
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I need to find somehow the analogous real symbolic solution(s) for the 4x4 symbolic matrix on the top. (Actually, s - is probability, a value in between 0 and 1, thus, can not be neither negative nor complex or whatever) I know that the solution of Ct*(P - 1) = 0 gives a symbolic vector Ct with real values, which equals to 1. I have a 2 x 2 stochastic matrix with the det= 0: If there is 1k possible solutions, I, actually, will be happy to get first 10 (that do differ from ).
#Matlab symbolic toolbox matrices software
If there are other software packages/libraries I could use in order to solve this particular problem ? For the moment, both Matlab and Mathematica give me solution.Ĭan I introduce somehow the criterion sum(X) = 1 in the search ? I may understand (as a person with a weak/"week" math background) that there may be no easy or trivial symbolic solution. I made the following Matlab code (created with a help of munity): clear all clc The determinant of P equals 0, and sum(X) should be equal 1. I need to find the symbolic null space vector (let's call it X ) of a symbolic matrix: P =