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6: Linear Maps - Mathematics


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 ),

[ egin{equation*}
left.
egin{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}
ight},
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.


Watch the video: Linear transformations and matrices. Chapter 3, Essence of linear algebra (November 2021).