The document defines the normal or canonical form of a matrix. It states that a matrix A of order mxn is in normal form if it can be reduced to the form [I|0] using elementary transformations, where I is the rxr identity matrix and r is the rank of the matrix. The normal form partitions the matrix into blocks with the identity matrix I containing the pivot positions and zeros elsewhere.

1. UNIT-I
Matrices
Dr.E.Prasad
Asst Professor, Dept of Mathematics
VNR VJIET
LINEAR ALGEBRA
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Dr.E.Prasad,Asst Professor

2. Lecture 2
Normal Form
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Dr.E.Prasad,Asst Professor

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Dr.E.Prasad,Asst Professor
Definition: If a matrix A of order mxn is reduced to the form ,
, , and ,
using a sequence of elementary transformations then it called
canonical or normal form. denotes identity matrix of order r
and the rank is r.
CANONICAL FORM Or NORMAL FORM

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Dr.E.Prasad,Asst Professor

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Dr.E.Prasad,Asst Professor

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Dr.E.Prasad,Asst Professor

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Dr.E.Prasad,Asst Professor

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Dr.E.Prasad,Asst Professor

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Dr.E.Prasad,Asst Professor

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Dr.E.Prasad,Asst Professor