Transpose of a Rectangular Matrix
The transpose of a matrix is obtained by interchanging its rows into columns or columns into rows. If “A” is any matrix of order “m × n,” then its transpose is represented either as A’ or AT. As the given matrix “A” has “m” rows and “n” columns, its transpose will have “n” rows and “m” columns. Have a look at the example given below to understand the transposition of a matrix.
[Tex]A = \left[\begin{array}{cccc} a & b & c & d\\ p & q & r & s \end{array}\right]_{2\times4} ⇒ A^{T} = \left[\begin{array}{cc} a & p\\ b & q\\ c & r\\ d & s \end{array}\right]_{4\times2}[/Tex]
Rectangular Matrix
A rectangular matrix is a matrix that is rectangular in shape. We know that the elements of a matrix are arranged in rows and columns. If the number of rows in a matrix is not equal to the number of columns in it then the matrix is known as a rectangular matrix.
Let us learn more about the rectangular matrix along with definitions, examples, properties, and operations on it.
Table of Content
- What is a Rectangular Matrix?
- Types of Rectangular Matrices
- Addition and Subtraction of Rectangular Matrices
- Multiplication of Rectangular Matrices
- Transpose of a Rectangular Matrix
- Properties of a Rectangular Matrix