Types of Matrices

Types of Matrices:

• Square matrix: A matrix with an equal number of rows and columns.
• Rectangular matrix: A matrix with a different number of rows and columns.
• Diagonal matrix: A square matrix with all elements outside the diagonal equal to zero.
• Identity matrix: A diagonal matrix with all diagonal elements equal to one.
• Triangular matrix: A square matrix where all elements below or above the diagonal are zero.

 

List of Formulas to remember:

Types of Matrices:

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• Row Matrix: $$[a_1, a_2, ..., a_n]$$

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• Column Matrix: $$\begin{bmatrix} a_1 \\ a_2 \\ \vdots \\ a_m \end{bmatrix}$$

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• Square Matrix: $$A = [a_{ij}]_{n \times n}$$

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• Diagonal Matrix: $$A = [a_{ij}] \text{ where } a_{ij} = 0 \text{ for } i \neq j$$

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• Identity Matrix: $$I_n = [a_{ij}] \text{ where } a_{ij} = 1 \text{ for } i=j \text{ and } a_{ij} = 0 \text{ for } i\neq j$$

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• Upper Triangular Matrix: $$A = [a_{ij}] \text{ where } a_{ij} = 0 \text{ for } i > j$$

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• Lower Triangular Matrix: $$A = [a_{ij}] \text{ where } a_{ij} = 0 \text{ for } i < j$$

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