low dimensional Archives - Infinity is Really Big

June 20, 2019September 12, 2019

Matrices and Linear Transformations in Low Dimensions

Visual Linear Algebra Online, Section 1.5

The null space (kernel) of the linear transformation defined by $T\left(\begin{array}{c} x \\ y \end{array}\right)=2x+y$ is a straight line through the origin in the plane ${\Bbb R}^{2}$ .

T\left(\begin{array}{c} x \\ y \end{array}\right)=2x+y — The null space (kernel) of the linear transformation defined by $T\left(\begin{array}{c} x \\ y \end{array}\right)=2x+y$ is a straight line through the origin in the plane ${\Bbb R}^{2}$ .

In mathematics, a matrix is not a simulated reality, but instead just a plain-old rectangular array of numbers. This does not mean, however, that mathematical matrices are uninteresting.

In fact, we … Read the rest