Types of Matrix

==2024-11-20

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Theory

1. Row matrix (Vector) $A_{1\times n}$

2. Column matrix (Vector) $A_{m\times 1}$

3. Square matrix $m=n$ in $A_{m\times n}$

4. Diagonal matrix $A_{m\times n}$ where $a_{ij}=0$ if $i\ne j$

5. Identity $A_{m\times n}$ where $a_{ij}=0$ if $i\ne j$ and $a_{ij}=1$ when $i=j$.

6. Scalar matrix $A_n$, where $A=k{I}_n$ , k is a scalar.

7. Upper Triangle Matrix $A_{m\times n}$ where $a_{ij}=0$ if $i,j<1$

8. Lower Triangle Matrix $A_{m\times n}$ where $a_{ij}=0$ if $i,j>1$

9. Zero $O$ or $\bar{0}$ Matrix $A_{m\times n}$ where $a_{ij}=0$. Role of zero → maintains position if element doesn’t exist.

10. Rectangular Matrix $m\ne n$ or $m=n$

11. Complex Matrix

12. Hermitian Matrix

13. Orthogonal Matrix

14. Unitary Matrix

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PTR