Posts Tagged ‘eigenvalue’
Friday, November 6th, 2009
Introduction to Invariants
Description
A detailed tutorial on invariants and the property of invariance. Step by step tutorial including several examples of invariants for reference.
Overview
Invariants are any function or number that displays the property of invariance. Invariance is when a function or number can go through several transformations without changing, or without going outside of its set parameters. The set parameters differ depending on the function or number. Some examples of invariant functions and numbers are the absolute value of a complex number, the degree of a polynomial, and certain parts of a square matrix
Tags: absolute, arithmetic, complex, degree, determinant, eigenvalue, eigenvector, function, invariance, invariant, matrix, number, parameters, polynomial, square, trace, transformations, value
Posted in Arithmetic | No Comments »
Tuesday, November 3rd, 2009
Eigenvalues and Eigenvectors Explained
Description
A detailed tutorial on eigenvalues and eigenvectors. Step by step tutorial including several examples of eigenvalues and eigenvectors for reference.
Overview
Eigenvalues and eigenvectors are related concepts commonly used in linear algebra. More specifically, they are properties of a matrix. They give very important information about a matrix, and are used in matrix factorization. Assuming that a matrix is a diagonal matrix (a square matrix or a similar matrix that you can calculate diagonals on), then the eigenvalues are the numbers on the diagonal and the eigenvectors are the basis vectors to which there numbers refer. You cannot have an eigenvector without an eigenvalue. However, you can have an eigenvalue without an eigenvector.
Tags: algebra, basis, diagonal, eigenvalue, eigenvector, factorization, linear, matrices, matrix, properties, square, transformations, vectors
Posted in Algebra | No Comments »
Tuesday, November 3rd, 2009
How to Find the Trace
Description
A detailed tutorial on find the trace of a matrix. Step by step tutorial including several examples of how to find the trace for reference.
Overview
The trace of a square matrix is defined to be the sum of the elements on the main diagonal of the matrix. This can be mathematically expressed as:
Remember, the trace is only defined for square matrices – not any other kind of matrix.
Tags: algebra, diagonal, eigenvalue, element, invariant, linear, main, matrices, matrix, Spur, square, sum, trace
Posted in Algebra | No Comments »
