Can anyone tell me The Role of Linear Algebra in Computer Science?
And also its application in computer science
- 1 decade agoFavorite Answer
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.
- Anonymous6 years ago
If you're doing anything with vectors mathematically, linear algebra is an efficient and powerful way to deal with that. And, the way computers go, any mathematics in a 2-dimensional or 3-dimensional world involve vectors.
3D game programming is the most visible and obvious application, where linear algebra is used for all placement, rotation, scale, camera orientation, physics, collision, and even lots of coloring operations.
Beyond that, again, anything having to deal with the physical world will probably use linear algebra in the computer application. Physics simulations, maybe stress testing, GPS data. Screensavers.
Most of the math can be done by libraries for you (DirectX for 3D game programming deals with all of the matrix operations, you just have to worry about a few of them), but a good solid knowledge of the concepts of linear algebra will give you a greater ability to code efficient and powerful code.
- mobletLv 41 decade ago
I'm not a computer scientist, but I know that graphics is one (transformations are used to alter scale, perspective, etc). The second link has examples of how linear and non-linear transformations can change the appearance of an image.Source(s): http://en.wikipedia.org/wiki/Transformation_matrix http://www-groups.dcs.st-and.ac.uk/~history/Miscel...
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- Anonymous1 decade ago
A computer chip is nothing but a matrix filled with 1's and 0's. Therefore, linear algebra is used to sort the 1's and 0's to make its calculations.
- oldprofLv 71 decade ago
There are several aspects of CS: hardware, software, peopleware. LA can be used in all three categories; for examples:
Hardware: optimal design for bit transmission rates/volumes, Kirchhoff's Law, etc.
Software: math operations on arrays, curvilinear coordinate transforms, etc.
Peopleware: optimal allocation of resources among software development teams
LA is a very powerful tool for solving allocations, optimization, and such for complex systems with multiple elements.Source(s): Taught LA at the MBA level.
- 1 decade ago
Matrix calculation is must for computer science.
- 1 decade ago
Allot of trigonometry geometry is used in game development.