Question

Define normal form of a matrix?

Answer 1

Normal form of a matrix is a matrix satisfying following conditions:

consist of only ones and zeros.

every row has a maximum of single one and rest are all zeros (there can be rows with all zeros).

We can produce the normal form of a matrix by doing row operations

Rank of a matrix can be found from its normal form by counting the number of rows with non zero elements. But you dont need to reduce to normal form, rank can also be found from echelon matrix, its much easier.

Answer 2

Matrix:

Any system of mn elements  arranged in a rectangular array in m rows and n columns is called a m × n matrix.

Normal form of a matrix :

A matrix A can be reduced by elementary row and column transformation into one of the following equivalent matrix.

• $\left[\begin{array}{ccc}I_{n}&:&0\\...&:&...\\0&:&0\end{array}\right]$      
• $\left[\begin{array}{c}I_{n}&...&0\end{array}\right]$
• $\left[\begin{array}{ccc}I_{n}&:&0\end{array}\right]$
• $\left[\begin{array}{c}I_{n}\end{array}\right]$

These forms are known as Normal Or Canonical form of matrix A.

where $I_{n}$ is n × n identity matrix and ) is null matrix or zero matrix of any order.

In general terms, Normal form of a matrix is a matrix of pre assigned special form obtained by means of transformations of a prescribed type.