Posts Tagged ‘space’
Friday, October 23rd, 2009
Introduction to the Four-Vector
Description
A detailed tutorial on the four-vector. Step by step tutorial including several examples of the four-vector and how to solve it for reference.
Overview
In linear algebra, a four-vector is defined as a vector in four-dimensional real vector space. The difference between a vector and a four-vector is that a four-vector can be transformed by Lorentz transformations. The concept of four-vectors branches out throughout vector mathematics, and to special relativity and general relativity. The concepts are a little different in each, but not enough to make it confusing if you are learning about them from a different standpoint. Four-vectors are often used in combination with matrices.
Tags: algebra, concept, four-dimensional, four-vector, general, Lorentz, matrices, real, relativity, space, special, transformations, vector
Posted in Algebra | No Comments »
Friday, October 23rd, 2009
Introduction to Vector Space
Description
A detailed tutorial on vector space. Step by step tutorial including several examples of vector space and how to solve for vector space for reference.
Overview
Vector space is simply a structure in mathematics that is formed by a collection of vectors. Vector space can be calculated using vector addition and scalar multiplication. Vector space is very dependent on the definition of a vector. Some vectors are simply arrows on a fixed plane. But in general, the term vector just means there is an object for which two operations can be performed. The definition of vector space is defined in algebraic terms, as opposed to the geometric terms that can sometimes be applied.
Tags: addition, algebra, arrow, collection, definition, Geometry, multiplication, object, operation, plane, scalar, space, vector
Posted in Algebra | No Comments »
Tuesday, September 22nd, 2009
How to Solve the Helmholtz Equation
Description
A detailed tutorial on the visual representation of the Helmholtz Equation. Step by step tutorial including several examples of the visual representation of the Helmholtz Equation for reference.
Overview
The Helmholtz Equation is an elliptic partial differential equation, which can be used to calculate waves. It is similar to the wave and heat equations in that manner, but the formula is very different. The formula can be expressed as 
where k is the wavenumber and A is the amplitude. The Helmholtz Equation is often used for problems involving partial differential equations in both space and time.
Tags: amplitude, elliptic, helmholtz, helmholtz equation, partial differential equations, Physics, Science, space, time, wavenumber, waves
Posted in Differential Equations | No Comments »
