Advanced Engineering Mathematics, 7th Edition

8.3 Rank of a Matrix

INTRODUCTION

In a general m × n matrix,

,

the rows

u₁ = (a₁₁ a₁₂ . . . a_1n), u₂ = (a₂₁ a₂₂ . . . a_2n), . . . , u_m = (a_m1 a_m2 . . . a_mn)

and columns

are called the row vectors of A and the column vectors of A, respectively.

A Definition

As vectors, the set u₁, u₂, . . . , u_m is either linearly independent or linearly dependent. We have the following definition.

DEFINITION 8.3.1 Rank of a Matrix

The rank of an m × n matrix ...