General matrix - If a set of m\[\times \]n number are arranged in m number of rows and n number of columns, is known as general matrix or rectangular matrix .
Example - Representation of 3\[\times \]4 matrix as an rectangular array.
\[ \begin{bmatrix}a_1 &a_2&a_3&a_4\\b_1&b_2&b_3&b_4\\c_1 &c_2&c_3&c_4\end{bmatrix}\]
Square Matrix- It is a Matrix with same number of rows and columns .
here m=n
Example-
Representation of 3\[\times \]3 matrix as an rectangular array.
\[ \begin{bmatrix}a_1 &a_2&a_3\\b_1&b_2&b_3\\c_1 &c_2&c_3\end{bmatrix}\]
order of square matrix is always n\[\times \]n
Upper triangular matrix - A matrix in which all the elements below diagonal elements are zero , is called upper triangular matrix
Example-\[ \begin{bmatrix}a_1 &a_2&a_3\\0&b_2&b_3\\0 &0&c_3\end{bmatrix}\]
Lower triangular matrix - A matrix in which all the elements above diagonal elements are zero , is called lower triangular matrix.
other elements may or may not be 0
Example-\[ \begin{bmatrix}a_1 &0&0\\b_1&b_2&0\\c_1&c_2&c_3\end{bmatrix}\]
Diagonal matrix - A square Matrix is said to diagonal matrix if all the non diadonal elements must be 0.
Ex- \[ \begin{bmatrix}a_1 &0&0\\0&b_2&0\\0 &0&c_3\end{bmatrix}\]
Note - It is a type of square matrix
Scalar Matrix - It is a type of diagonal matrix in which all the diagonal elements are same .
Ex-\[ \begin{bmatrix}a &0\\0&a\end{bmatrix}\]
Unit matrix- A diagonal matrix wherein all the diagonal elements are 1 , is called unit matrix.
Ex- \[ \begin{bmatrix}1 &0&0\\0&1&0\\0 &0&1\end{bmatrix}\] of order 3\[\times \]3
Column Matrix - A matrix havng only one column is called colums matrix.
Note - order of colums matrix is always n\[\times \]1 where n is number of rows
Ex-\[\begin{bmatrix}2\\3\\8\\0\\9\end{bmatrix}\]
Row Matrix- A matrix with only one row is called Row Matrix.
Note - order of colums matrix is always 1\[\times \]n where n is number of columns
Ex-\[\begin{bmatrix}2&4&4&5&5&0\end{bmatrix}\]
