The Inverse Matrix of a Linear Transformation
Visual Linear Algebra Online, Section 1.9
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 have inverse functions. Those that … Read the rest
Matrix Multiplication and Composite Transformations
Visual Linear Algebra Online, Section 1.8
Function composition is a fundamental binary operation that arises in all areas of mathematics. Function composition is a useful way to create new functions from simpler pieces.
When the functions are linear transformations… Read the rest
High-Dimensional Linear Algebra
Visual Linear Algebra Online, Section 1.7
Many practical situations that require the use of linear algebra can involve hundreds or even thousands of unknowns. Modeling a national economy, optimizing the purchase of supplies, and managing flight schedules are prominent examples.
A vector quantity representing all the data in such a situation might therefore … Read the rest
Linear Algebra in Three Dimensions
Visual Linear Algebra Online, Section 1.6
Linear algebra has immense practical value in our modern world. Statistics, business, science, and engineering all make heavy use of the
Matrices and Linear Transformations in Low Dimensions
Visual Linear Algebra Online, Section 1.5
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