Matrici – ValCon.It

Considera matrici quadrate di dimensione 2, 3, …

$\displaystyle A = \begin{bmatrix}a_{11} & a_{12} & a_{13} \\a_{21} & a_{22} & a_{23} \\a_{31} & a_{32} & a_{33}\end{bmatrix}$

$\displaystyle B = \begin{bmatrix}b_{11} & b_{12} & b_{13} \\b_{21} & b_{22} & b_{23} \\b_{31} & b_{32} & b_{33}\end{bmatrix}$

Matrice nulla

$\displaystyle \textbf{0} = \begin{bmatrix}0 & 0 & 0 \\0 & 0 & 0 \\0 & 0 & 0\end{bmatrix}$

Proprietà

$\displaystyle a_{ij} = 0$

$\displaystyle \textbf{I} = \begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{bmatrix}$

Proprietà

$\displaystyle a_{ij} = \begin{cases}1 & i=j \\0 & i\ne j\end{cases}$

Matrice diagonale principale

$\displaystyle \begin{bmatrix}a_{11} & 0 & 0 \\0 & a_{22} & 0 \\0 & 0 & a_{33}\end{bmatrix}$

Proprietà

$\displaystyle a_{ij} = \begin{cases}... & i=j \\0 & i\ne j\end{cases}$

Matrice diagonale secondaria (antidiagonale)

$\displaystyle \begin{bmatrix}0 & 0 & a_{13} \\0 & a_{22} & 0 \\a_{31} & 0 & 0\end{bmatrix}$

Proprietà

$\displaystyle a_{ij} = \begin{cases}... & i+j=n+1 \\0 & i+j\ne n+1\end{cases}$

Matrice triangolare superiore

$\displaystyle \begin{bmatrix}a_{11} & a_{12} & a_{13} \\0 & a_{22} & a_{23} \\0 & 0 & a_{33}\end{bmatrix}$

Proprietà

$\displaystyle a_{ij} = \begin{cases}... & i\le j \\0 & i > j\end{cases}$

Matrice triangolare inferiore

$\displaystyle \begin{bmatrix}a_{11} & 0 & 0 \\a_{21} & a_{22} & 0 \\a_{31} & a_{31} & a_{33}\end{bmatrix}$

Proprietà

$\displaystyle a_{ij} = \begin{cases}... & i\ge j \\0 & i < j\end{cases}$