The quantum chaos is related to a Gaussian random matrix model, which shows dip-ramp-plateau behavior in the spectral form factor for large size $N$. of time dependent model also with rounding instead kink near Heisenberg time. This converted two made $M_1$ and $M_2$. numerical evaluation finite $N$ analytic expression are compared factor.

Consider the most general 3 x 3 Majorana neutrino mass matrix M. Motivated by present neutrino-oscillation data, much theoretical effort is directed at reducing it to a specific texture in terms of a small number of parameters. This procedure is often ad hoc. I propose instead that for any M one may choose, it should satisfy the condition UMU(T)=M, where U not equal 1 is a specific unitary matr...

The Constant-Ratio Rule (CRR), an empirical technique for analysis of confusion matrices, was developed for use in predicting intelligibility of speech syllables. This study investigated the validity of the rule when applied to the data from experiments on visual form perception. English letters and simple geometric figures were tachistoscopically presented in the center of a viewing field. Res...

In this note we will discuss the structure theorem for finitely generated modules over a principal ideal domain from the point of view of matrices. We will then give a matrixtheoretic proof of the structure theorem from the point of view of the Smith normal form of a matrix over a principal ideal domain. One benefit from this method is that there are algorithms for finding the Smith normal form...

the principle of dimensionality reduction with pca is the representation of the dataset ‘x’in terms of eigenvectors ei ∈ rn  of its covariance matrix. the eigenvectors oriented in the direction with the maximum variance of x in rn carry the most      relevant information of x. these eigenvectors are called principal components [8]. assume that n images in a set are originally represented in mat...

In this note we will discuss the structure theorem for finitely generated modules over a principal ideal domain from the point of view of matrices. We will then give a matrixtheoretic proof of the structure theorem from the point of view of the Smith normal form of a matrix over a principal ideal domain. One benefit from this method is that there are algorithms for finding the Smith normal form...