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 …

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 …

Application of Linear Algebra in Computer Graphics

application of linear algebra in computer graphics

The first use of Linear Algebra can be seen in the polygonal structure of 3D characters and space in computer games and other 3D graphics applications. Polygons are used to make images look three-dimensional because of their geometric structures. Most of the time, this is done by dividing the object into smaller and smaller polygons where the given smaller parts are triangular. This makes the production of 3D objects part of the distribution process of polygons. A simple example of the use of polygons in 3D images in the form of object frame.

How to diagonalize a matrix? Example of diagonalization

Diagonalization of a matrix How to diagonalize a matrix? Example of diagonalization. An nxn matrix A is said to be diagonalizable if there exists an invertible matrix P such that A=PDP–. Procedure for diagonalizing a matrix For diagonalizing a matrix Read More …