What is the Gram Schmidt Procedure? Explanation and Example

gram schmidt procedure demonstration

Since, by applying head to tail rule on the vectors components, we can generate the original vector A. After that we need to find the projections of one vector to another vector. This projection is subtracted from the other vector and hence these two vectors become orthogonal.

So, for two vectors A and B lets say we want to generate a new set of vectors W and Y that will be orthogonal to each other. We will assume

How to test that the Given Vectors are Linearly Independent or Dependent?

linearly independent vectors

Linearly Independent Vectors: How to test the given vectors are linearly independent or not? The vectors v1,v2,v3,…vn in a vector space V are said to be linearly dependent if there exist constants c1,c2,c3,….cn not all zero such that: c1v1+c2v2+c3v3+……+cnvn=0  ————————-(i) Read More …

Singular Value Decomposition with Eigen Value Equal to 0

Singular Value Decomposition Example Singular Value Decomposition (SVD) is a fundamental technique in linear algebra with applications in various fields such as signal processing, statistics, machine learning, and data analysis. It is a method to decompose a matrix into three Read More …

The fast Fourier transform method and ill-conditioned matrices

FFT and Ill-conditioned Systems

Introduction The fast Fourier transform method and ill-conditioned matrices. We have studied the problem of calculating numerical solutions of the linear algebra equation, a*x=b, where a denotes an N*N ill-conditioned coefficient matrix. It is known that Gaussian elimination methods linked Read More …