Wavelets may have a graph that looks a bit like this.
Wavelets are one of the new hot topics in mathematics as of July 2010. They first began to be of real interest in the 1980s, when they were viewed as an alternative to Fourier analysis. They have many applications both in pure mathematics, such as in differential equations, and in the real world for things like image compression.
What Are Wavelets?
Wavelets, as their name implies, are little waves. More specifically, they are oscillatory functions that increase and decrease.
History
Wavelets first began to be studied in the 1930s. They were an offshoot of Fourier analysis. Fourier analysis is a representation of a function as a series. These series can then be used to analyze signals, much like wavelets. In the 1930s, wavelets were found only in the realm of pure math. However, by the 1980s, many real-world applications had been found for wavelets.
Applications
You can find applications for wavelets in many diverse fields. As of 2010, they are used in image compression, quantum physics, signal processing and seismic geology. The wavelets can be used to describe how an electric signal behaves.
Linear Algebra
Linear algebra is usually studied as an undergraduate. If you are a math major, it falls into the range of pure mathematics. You will not only be studying lines, but all functions whose exponential value is one. Vectors and matrices are important components of linear algebra.
Wavelet Transforms and Linear Algebra
You can study the wavelet transformations by using the inner product in linear algebra. The resulting vectors can then be stored in a matrix and used for various applications.
Why From a Linear Algebra Perspective?
Wavelets can be a rather complicated concept, difficult for the undergraduate to understand. By introducing them through linear algebra, it gives you the chance to assimilate the basic idea of this complex concept with an idea you have already studied.
Tags: Fourier analysis, first began, image compression, pure mathematics
