Definitions [3]
Definition: Matrix
A matrix is a rectangular arrangement of numbers arranged in rows and columns, enclosed in brackets [ ] or parentheses ( ).
Elements (Entries) of a Matrix
- Each number in a matrix is called an element (or entry).
Rows and Columns
- Horizontal lines → rows
- Vertical lines → columns
Order of a Matrix
- Order = number of rows × number of columns
- Written as m × n and read as “m by n”
Definition: Equality of Matrices
Two matrices are equal if and only if:
- They have the same order (same number of rows and columns), and
- Their corresponding elements are equal.
Example:
\[A=
\begin{bmatrix}
2 & & 3 \\
1 & & 5
\end{bmatrix}\mathrm{and} B=
\begin{bmatrix}
2 & & 3 \\
1 & & 5
\end{bmatrix}\]
Definition: Transpose of a Matrix
The transpose of a matrix is obtained by interchanging its rows and columns.
-
If a matrix is A, its transpose is denoted by AT
-
If A is of order m × n, then
AT is of order n × m - First row of A becomes first column of AT, and so on.
Key Points
Key Points: Types of Matrices
| Type of Matrix | Key Property |
|---|---|
| Row Matrix | Has only one row (1 × n) |
| Column Matrix | Has only one column (m × 1) |
| Square Matrix | Number of rows = number of columns (n × n) |
| Rectangular Matrix | Number of rows ≠ , number of columns |
| Zero (Null) Matrix | All elements are 0 |
| Diagonal Matrix | Square matrix; all non-diagonal elements = 0 |
| Unit (Identity) Matrix | Diagonal matrix with all diagonal elements = 1 |
