Linear algebra is the study of Linear equations, matrix, determinants, and vectors spaces. The results of linear algebra have found application in such diverse fields as optics, quantum mechanics, display addressing, electric circuits, cryptography, computer graphics, economics, linear programming, solution of systems of differential equations, etc. The manipulation of matrices and determinants plays a central role in all applications of linear algebra.
Linear algebra has a great role in: Mathematics, Computer graphics, Data Compression, Network Flow etc
Linear Algebra is one of the most important areas in mathematics, with numerous applications in an extremely wide spectrum of disciplines in Science & Engineering. The language of vectors and matrices is an elegant way to describe (among other things) the way in which an object may be rotated, shifted (translated), or made larger or smaller (scaled).
Image (jpg), video (MPG) and compression algorithms make use of Fourier transform a linear transformation. In all cases, the compression makes use of the fact that in Fourier space information can be cut away without disturbing the main information.
Computer graphics uses linear algebra like matrix algebra, change of coordinates, geometry and 3-dimensional calculus. Also we can scale an object we can translate an object or we can rotate an object .Via linear matrix we can draw the pixels. The ideas of linear algebra are used throughout computer graphics. In fact, any area that concerns itself with numerical representations of geometry often will collect together numbers such as x,y,z positions into mathematical objects called vectors. Vectors and a related mathematical object called a matrix are used all the time in graphics.
Linear programming uses a system of inequalities called constraints to maximize profit functions and minimize cost functions. all such problem occurring in industry are solved by a computer using linear algebra.
The importance of linear algebra for applications has raisin in direct proportion to the increase in computing power. With each new generation of hardware and software trigging a demand for even great capabilities. Computer science this intricately linked with linear algebra through the explosive growth of parallel processing and large scale computation.