6: Linear Maps
- Page ID
- 270
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As discussed in Chapter 1, one of the main goals of Linear Algebra is the characterization of solutions to a system of \(m \) linear equations in \(n \) unknowns \( x_1, \ldots, x_n \),
\[ \begin{equation*}
\left.
\begin{array}{rl}
a_{11} x_1 + \cdots + a_{1n} x_n &= b_1\\
\vdots \qquad \vdots \qquad & \quad \vdots\\
a_{m1} x_1 + \cdots + a_{mn} x_n &= b_m
\end{array}
\right\},
\end{equation*} \]
where each of the coefficients \(a_{ij} \) and \(b_i \) is in \(\mathbb{F} \). Linear maps and their properties give us insight into the characteristics of solutions to linear systems.
Contributors
- Isaiah Lankham, Mathematics Department at UC Davis
- Bruno Nachtergaele, Mathematics Department at UC Davis
- Anne Schilling, Mathematics Department at UC Davis
Both hardbound and softbound versions of this textbook are available online at WorldScientific.com.