1.3 Some Particular Matrices


Name	Definition	Notation	Trivial Example

Scalar	\(p=n=1\)	\(a,b\)	\((1)= 1\)

Square	\(p=n\)	\(A_{p\times p}\)	\( \begin {pmatrix} 1 & 3\\ 4 & 5\\ \end {pmatrix}_{2\times 2} \)

Diagonal	\(p=n, a_{ij}=0, i\neq j\)	\(Diag(a_{ij})\)	\( \begin {pmatrix} 2 & 0\\ 0 & 4\\ \end {pmatrix} \)

Identity	\(Diag(1)\)	\(I\) or \(I_p\)	\( \begin {pmatrix} 1 & 0\\ 0 & 1\\ \end {pmatrix} \)

Symmetric	\(a_{ij} = a_{ji}\)		\( \begin {pmatrix} 1 & 2\\ 2 & 1\\ \end {pmatrix} \)

Unit matrix	\(p=n, a_{ij}=1\)	\(J_p = \underline {1}\,\underline {1}'\)	\( \begin {pmatrix} 1 & 1\\ 1 & 1\\ \end {pmatrix} \)

Triangular	\(a_{ij} = 0\)	\(\Delta \)	\(\begin {pmatrix} 1 & 0 & 0\\ 2 & 2 & 0\\ 3 & 2 & 5\\ \end {pmatrix} \)
	below/ above the
	diagonal
Asymmetric	\(a_{ij} \neq a_{ji}\)		\(\begin {pmatrix} 1 & 1\\ 2 & 3\\ \end {pmatrix}\)

Null	\(a_{ij} =0\)	0	\(\begin {pmatrix} 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0\\ \end {pmatrix}\)

Table 2:

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