Principal Component Analysis (PCA) Principal Component Analysis is a technique for simplifying datasets. It is a linear transformation that transforms the data into a new coordinate system such that the first largest variance of any da 2022-07-11 Blog Linear Algebra
Singular Value Decomposition (SVD) Part 2 In Singular Value Decomposition (SVD) Part 1, I introduce one way to calculate SVD. And in this post, I would talk about other ideas about solving SVD. Matrix AAA is symmetric A⋅(q1,…qn)=(λ1q1…λnqn)= 2022-07-08 Blog Linear Algebra
Tensor Operation In machine learning/big data we can think of a tensor as an nD-array. The picture below is an example of a rank 3 tensor with size (3,4,2). Tensor unfolding Unfolding a tensor to a matrix (“matrizat 2022-07-06 Blog Linear Algebra
QR Decomposition The QR (orthogonal triangular) decomposition is the most effective and widely used method to find all the eigenvalues of a general matrix. It decomposes the matrix into a normal orthogonal matrix QQQ 2022-06-28 Blog Linear Algebra
The Least Squares Problem The Least Squares Problem is one of the most important problem in numerical approximation. The main idea of the least squares problem is to solve the unknown parameters , so that the sum of the square 2022-04-16 Blog Linear Algebra
Cholesky Decomposition Cholesky decomposition is to express a symmetric positive definite matrix as a decomposition of the product of a lower triangular matrix and its transpose. It requires that all eigenvalues of the matr 2022-04-15 Blog Linear Algebra
LU Decomposition LU decomposition is a common method to solve polynomial Ax=bAx=bAx=b, and this method is consist of three steps: (1) LU factorization: Gaussian elimination on matrix AAA, factorize AAA to L,UL,UL,U su 2022-04-14 Blog Linear Algebra
Introduction to Docker-Compose Docker-Compose is used to manage your containers, kind of like a container steward. We write a file, declare the container to be started in this file, configure some parameters, execute this file, Doc 2022-04-13 Blog Docker
Basic Use of Docker Docker is an open source application container that allows developers to package their applications and dependencies into a portable engine, and then publish them to operating system such as Linux or 2022-04-13 Blog Docker
Norms and Condition Number Norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways, which can be used to measure the size of vectors (vector norm) and matrices (matri 2022-03-28 Blog Linear Algebra
