Category:Definitions/Null Spaces
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This category contains definitions related to Null Spaces.
Related results can be found in Category:Null Spaces.
Let:
$\quad \mathbf A_{m \times n} = \begin {bmatrix}
a_{11} & a_{12} & \cdots & a_{1n} \\
a_{21} & a_{22} & \cdots & a_{2n} \\
\vdots & \vdots & \ddots & \vdots \\
a_{m1} & a_{m2} & \cdots & a_{mn} \\
\end {bmatrix}$, $\mathbf x_{n \times 1} = \begin {bmatrix} x_1 \\ x_2 \\ \vdots \\ x_n \end {bmatrix}$, $\mathbf 0_{m \times 1} = \begin {bmatrix} 0 \\ 0 \\ \vdots \\ 0 \end {bmatrix}$
be matrices where each column is a member of a real vector space.
The set of all solutions to $\mathbf A \mathbf x = \mathbf 0$:
- $\map {\mathrm N} {\mathbf A} = \set {\mathbf x \in \R^n : \mathbf {A x} = \mathbf 0}$
is called the null space of $\mathbf A$.
Pages in category "Definitions/Null Spaces"
The following 4 pages are in this category, out of 4 total.