# Nullity And Rank Of A Linear Transformation

In this article we will learn about nullity and rank of a linear transformation.

Definition

Let V and W be vector spaces over the field

Skip to content
# Category: Linear Algebra

# Nullity And Rank Of A Linear Transformation

# Kernel Of Linear Transformation

# Introduction To Linear Transformation

# Dimension Of Vector Space

# What is the Basis of Vector Space

# Linear Dependence and Linear Independence of Vectors

# Linear Span / Generator of Vector Space

# All You Need To Know – Subspace of Vector Space

# Introduction To Vector Space In Linear Algebra

In this article we will learn about nullity and rank of a linear transformation.

Definition

Let V and W be vector spaces over the field

Kernel Definition

Let V and W be vector spaces over a the field F and T: V → W be a linear transformation, The kernel

Linear Transformation Definition

Let V and W be vector spaces over the field F, a transformation T from V to W is said to be

Definition of Dimension of a Vector Space

If a vector space V over a field F has a basis consisting of a finite number of

Basis of a vector space

A basis of a vector space is a set of vectors of the space that (i) are linearly independent and

In this article we will learn linear dependence and linear independence of vectors.

Linear Dependence

For a vector space V defined over a field F,

Before discussing about linear Span we have to learn Linear Combination of vectors.

Linear Combination Definition

Let V be vector space over a field F.

Subspace of Vector Space

If V is a vector space over a field F and W ⊆ V, then W is a subspace of vector

Introduction

Here we introduce a general mathematical concept, called vector space.

In the study of mathematics we encounter many examples of mathematical objects that can