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Gradient of Vector Calculus
The gradient is a fancy word for derivative, or the rate of change of a function. It’s a vector (a direction to…
basic 1 min read
Cayley-Hamilton Theorem
Given (1) (2) then (3) where is the identity matrix. Cayley verified this identity for and 3 and postulated that it was true…
basic 2 min read
Matrix Diagonalization
Matrix diagonalization is the process of taking a square matrix and converting it into a special type of matrix–a so-called diagonal matrix–that shares…
basic 3 min read
Eigenvalues and Eigenvectors
Introduction This page is a brief introduction to eigenvalue/eigenvector problems (don’t worry if you haven’t heard of the latter). Before…
basic 2 min read
Determinant of a Matrix
The determinant of a matrix is a special number that can be calculated from a square matrix. A Matrix is an array of numbers: A…
basic 3 min read
Matrix Inverse
This lesson defines the matrix inverse, and shows how to determine whether the inverse of a matrix exists. Matrix Inversion Suppose A is an n x n matrix.…
basic 2 min read
Algebra of Matrices
Algebra of Matrices is the branch of mathematics, which deals with the vector spaces between different dimensions. The innovation of matrix…
basic 2 min read
Curl Of A Vector Function
Suppose I have a vector such as . Now the curl of this vector will be So if I evaluate the determinant, I’ll get…
basic 1 min read
Divergence Of A Vector Function
Suppose I have a vector such as . Now the divergence of this vector will be So if I use the technique for first-order…