MATLAB: How to find lambda from this formula

eigenvaluematrix

det (A – lambda * I) = 0

where:

A= a square matrix, ex: [2 5 4;8 6 9;3 4 6]

I= identity matrix

Best Answer

e = eig(A) returns a vector of eigenvalues of the matrix A. To get the associated eigenvectors, use [V,D] = eig(A). See the documentation for eig to interpret V and D.

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MATLAB: Right eigenvector corresponding to an eigenvalue 1

As the documentation for the eig function says:

[V,D] = eig(A) returns diagonal matrix D of eigenvalues and matrix V whose columns are the corresponding right eigenvectors, so that A*V = V*D.

So, if you use the command above, for example

D(2,2) would give you the 2nd eigenvalue
V(:,2) would give you the 2nd eigenvector

- Sebastian

MATLAB: How to determine if a matrix is positive definite using MATLAB

This change has been incorporated into the documentation in Release 14 Service Pack 3 (R14SP3). For previous releases, read below for any additional information:

Rather than using the EIG function to obtain the eigenvalues in order to determine positive definiteness, it is more computationally efficient to use the CHOL function. The CHOL function provides an optional second output argument "p" which is zero if the matrix is found to be positive definite. If the input matrix is not positive definite, then "p" will be a positive integer:

 >>[~,p] = chol(zeros(3))
 p =
        1

The CHOL function will return an error if it is only provided with a single output argument, and is also given a matrix that is not positive definite. NOTE: CHOL expects its input matrix to be symmetric and only looks at the upper triangular portion of the matrix.

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Related Solutions

MATLAB: Right eigenvector corresponding to an eigenvalue 1

MATLAB: How to determine if a matrix is positive definite using MATLAB

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