A Blog on Applied Mathematics Aravindh Krishnamoorthy Website: https://sites.google.com/view/aravindhkrishnamoorthy Preface A collection of nifty results. Contents 1 Linear Algebra 1.1 Inverse Cholesky Factor of a positive definite Hermitian symmetric Toeplitz matrix using Durbin recursions 1.2 Complex-valued Durbin Algorithm with MATLAB code 1.3 Determinant Form for KummerU Function of a Matrix Argument 1.4 Offset Non-Uniform Discrete Cosine Decomposition of Toeplitz Matrices 1.5 Simultaneous Triangularization of Two Arbitrary Wide Matrices via the QR Decomposition 1.6 Cyclic Shifts Property of Trace with Hadamard Products 2 Probability Theory 2.1 Entropy of Uniformly Quantized Random Variables 2.2 Exact Formula for Asymptotic Convergence of Fourier Transform of Uniform Random Variables 2.3 Generating and Sampling Two Signed Bernoulli Random Variables with Given Correlation 2.4 Distribution of A Simple Function of Gamma Variables 2.5 Distribution of the Determinant of a Complex-Valued Sample Correlation Matrix 3 Random Matrix Theory 3.1 Stochastic Properties of Random Matrix Factors 3.2 Ordered densities of squared singular values of a Gaussian matrix product 4 Errata for Publications 4.1 Uplink and Downlink MIMO-NOMA with Simultaneous Triangularization 4.2 Downlink MIMO-RSMA with Successive Null-Space Precoding 5 License Bibliography