Recently I have tried to learn the concepts of Eigen Values and Vectors and I have currently managed to calculate the Eigen values and vectors based off a 2x2 matrix based off calculating the covariance matrix etc..
My problem is, I'm currently trying to perform analysis of a spectrogram, and, the dimensions for this data is 451x128 but I've only ever seen material related to calculating the eigen values and vectors based on 2x2 and 3x3.
Is it possible to be able to calculate such based on such high dimensional data?
The spectrogram data looks something as follows:
0.0009 0.0057 0.0049 0.0014 0.0053 0.0017 0.0026 0.0017
0.0035 0.0001 0.0009 0.0022 0.0002 0.0008 0.0019 0.0022
0.0026 0.0008 0.0001 0.0031 0.0052 0.0071 0.0055 0.0028
0.0024 0.0019 0.0080 0.0040 0.0006 0.0001 0.0001 0.0021
0.0133 0.0071 0.0033 0.0006 0.0002 0.0004 0.0011 0.0018
When I calculate the covariance matrix, assuming the 2x2 principle then I get the following:
Eigen Values: 22.58347e-06 1.09907e-07
Eigen Vectors: 0.941228 -0.337771
Whereas matlab gives me a completely different dimensionality when computing the eigen values and vectors.
Eigenvalues and eigenvectors are defined for squared matrix only. In the case of non-squared matrix we talk about singular values and singular vectors. Algorithm for computing singular vectors and values exists and are well-studied. See Singular Value Decomposition (SVD on matlab).