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Linear transformations can be very important in graphics. Also, linear transformations come up whenever you need to solve systems of linear equations, which arise quite often. Finally, they can be useful in further areas of mathematics such as topology.

Q: What are the applications of linear transformations?

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Linear programming approach does not apply the same way in different applications. In some advanced applications, the equations used for linear programming are quite complex.

Accurate linear measurement.

The applications are in finding optimum solutions to a linear objective function, subject to a number of linear constraints.

If the two equations are linear transformations of one another they have the same solution.

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Correlation has no effect on linear transformations.

Linear algebra is restricted to a limited set of transformations whereas algebra, in general, is not. The restriction imposes restrictions on what can be a linear transformation and this gives the family of linear transformations a special mathematical structure.

A matrix is a field of numbers with rows and columns. Matrices can represent many different things and have numerous applications. For example, they can be used for solving systems of linear equations or working with linear transformations; in multiple regression analyses, for working with vectors.

Rotations, reflections and enlargements.

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P. M. van Loon has written: 'Continuous decoupling transformations for linear boundary value problems' -- subject(s): Boundary value problems, Differential equations, Linear, Linear Differential equations, Transformations (Mathematics)

Linear programming approach does not apply the same way in different applications. In some advanced applications, the equations used for linear programming are quite complex.

Charles Gordon Cullen has written: 'Matrices and linear transformations'

Jet Wimp has written: 'Sequence transformations and their applications' -- subject(s): Acceleration of convergence, Numerical analysis, Sequences (Mathematics), Transformations (Mathematics)

Linear Algebra is a special "subset" of algebra in which they only take care of the very basic linear transformations. There are many many transformations in Algebra, linear algebra only concentrate on the linear ones. We say a transformation T: A --> B is linear over field F if T(a + b) = T(a) + T(b) and kT(a) = T(ka) where a, b is in A, k is in F, T(a) and T(b) is in B. A, B are two vector spaces.

Accurate linear measurement.

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