determinant Archives - Infinity is Really Big

August 29, 2019October 2, 2020

The Determinant of a Square Matrix

Visual Linear Algebra Online, Section 1.10

The absolute value of the determinant of a <img src='https://s0.wp.com/latex.php?latex=2%5Ctimes+2&bg=ffffff&fg=000000&s=0' alt='2\times 2' title='2\times 2' class='latex' /> matrix gives the area of the parallelogram determined by its column vectors. — The absolute value of the determinant of a $2\times 2$ matrix gives the area of the parallelogram determined by its column vectors.

2\times 2 — The absolute value of the determinant of a $2\times 2$ matrix gives the area of the parallelogram determined by its column vectors.

Mathematical beauty arises in many ways, though for most people, it is typically tied to something visual. The beauty of the more austere realm of abstract mathematics usually takes more time to appreciate

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July 29, 2019September 24, 2019

The Inverse Matrix of a Linear Transformation

Visual Linear Algebra Online, Section 1.9

The inverse of a rotation is another rotation by the same angle, but in the opposite direction.

Inverse functions are a kind of high-technology in mathematics. They can help you solve infinitely many problems at once!

In linear algebra, some linear transformations on finite-dimensional Euclidean space ${\Bbb R}^{n}$ have inverse functions. Those that … Read the rest

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