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 Novel Numerical Linear Algebra Algorithms 1.2 Determinant Form for KummerU Function of a Matrix Argument 1.3 Novel Matrix Decompositions 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 Distributions of Functions of Random Variables and Matrices 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