The eigenvalues of a square matrix with real entries can be complex. For example, a quick calculuation will verify that the eigenvalues of $$A = \begin{pmatrix} 1&-2\\2&1\end{pmatrix}$$ are $1\pm2i$. But when the matrix is symmetric, the eigenvalues must be real.…Continue readingEigenvalues of Real Symmetric Matrices
To solve a linear system of the form $A\vec x = \vec b$ we could use row reduction or, in theory, calculate $A^{-1}$ and use it to determine $\vec x$ with the equation $$\vec x = A^{-1} \vec b$$ But…Continue readingThe LU Factorization
Linear transformations are often used in computer graphics to simulate the motion of an object. They can be computed using a matrix-vector product of the form $$T(\vec x) = A\vec x$$ where $\vec x$ is a vector that represents a…Continue readingApplying Matrix Multiplication to 2D Computer Graphics
