basic

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…

Taylor’s theorem

Cayley-Hamilton Theorem

Given (1) (2) then (3) where  is the identity matrix. Cayley verified this identity for  and 3 and postulated that it…

<strong>Matrix Diagonalization</strong>

Matrix diagonalization is the process of taking a square matrix and converting it into a special type of matrix–a so-called diagonal…

Eigenvalues and Eigenvectors

Introduction This page is a brief introduction to eigenvalue/eigenvector problems (don’t worry if you haven’t heard of the…

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…

System of linear equations

Matrix Inverse

This lesson defines the matrix inverse, and shows how to determine whether the inverse of a matrix exists. Matrix Inversion…

Algebra of Matrices

Algebra of Matrices is the branch of mathematics, which deals with the vector spaces between different dimensions. The innovation…

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,…