Introduction to row spaces, columns spaces and null spaces For any given matrix ‘A’ of order mxn, there are three types of spaces associated to them: row(A), col (A), and null (A). These spaces are linked with the solution of Read More …

# Category: Linear Algebra

## what are the linearly dependent and independent vectors?

Linearly Independent Vectors: what are the linearly dependent and independent vectors? 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) otherwise v1,v2,v3,…..vn are Read More …

## How to find the basis of a vector space?

How to find the basis of a vector space? In order to find the basis of a vector space, we need to check two properties: The vectors should be linearly independent. These vectors should span in that vector space. If Read More …

## What is the span of a vector space?

Introduction to span of a vector space For the given set of vectors v1,v2,v3,……vn that belong to a vector space V and non-zero constants c1,c2,c3,….cn if they can generate another vector x(x1,x2) using the relation c1v1+c2v2+c3v3+…….+cnvn=x then we will say Read More …

## What are the vector spaces?

Introduction to Vector Space What are the vector spaces? The collection of vectors (V1,V2,V3,…..) are said to form a vector space (V) if the following properties are satisfied For any two vectors u,v that belongs to V, u+v should also Read More …

## How to diagonalize a matrix ?

Diagonalization of a matrix How to diagonalize a matrix ? 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 A, the Read More …

## What are the similar matrices?

Introduction to similar matrix and similar matrix transformation What are the similar matrices? Two square matrices A and B of the same order nxn are said to be similar if there exists an invertible matrix P such that B=P-1AP. It can Read More …

## How to calculate eigen values and eigen vectors of a matrix?

Introduction to eigen values and eigen vectors How to calculate eigen values and eigen vectors? Eigen Values and Eigen Vectors has a great significance in many engineering problems specially case of linear systems where we want to study the “change”. Read More …

## Application of linear algebra in cryptography

Application of linear algebra in cryptography Application of linear algebra in cryptography. Linear algebra is widely used in many engineering applications. The most common examples are: network solving, chemical equation balancing, engineering economy and in network security. With the advancement Read More …

## What are the nodal incident matrices?

What are the nodal incident matrices? Nodal incident matrices (NIM) are used for electrical network modeling. Any network consisting of larger number of branches or edges and nodes can be modeled through them. The purpose of modeling is to study Read More …