\(\DeclarePairedDelimiterX{\Set}[2]{\{}{\}}{#1 \nonscript\;\delimsize\vert\nonscript\; #2}\) \( \DeclarePairedDelimiter{\set}{\{}{\}}\) \( \DeclarePairedDelimiter{\parens}{\left(}{\right)}\) \(\DeclarePairedDelimiterX{\innerproduct}[1]{\langle}{\rangle}{#1}\) \(\newcommand{\ip}[1]{\innerproduct{#1}}\) \(\newcommand{\bmat}[1]{\left[\hspace{2.0pt}\begin{matrix}#1\end{matrix}\hspace{2.0pt}\right]}\) \(\newcommand{\barray}[1]{\left[\hspace{2.0pt}\begin{matrix}#1\end{matrix}\hspace{2.0pt}\right]}\) \(\newcommand{\mat}[1]{\begin{matrix}#1\end{matrix}}\) \(\newcommand{\pmat}[1]{\begin{pmatrix}#1\end{pmatrix}}\) \(\newcommand{\mathword}[1]{\mathop{\textup{#1}}}\)
Needs:
Real Affine Sets
›
Real Matrices
›
Needed by:
Real Affine Sets and Hyperplanes
›
Links:
Sheet PDF
›
Graph PDF
›
Real Affine Sets and Linear Equations
Main result
$M \subset \R ^{n}$ is affine if and only if there exists $b \in \R ^m$ and $B \in \R ^{m \times n}$ such that
\[ M = \Set*{x \in \R ^{n}}{Bx = b}. \]
Real Affine Sets and Linear Equations
Links:
Sheet PDF
›
Graph PDF
›
Needs:
Real Affine Sets
›
Real Matrices
›
Needed by:
Real Affine Sets and Hyperplanes
›
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