LinTrans Linear transformation on a vector space

Linear transformations in R^N or C^N. Wraps the functionality of Matrix to be able to easitly multiply matrixes with vectors (classes inheriting from AbstractVector). A LinTrans holds a matrix that represents the linear transformation.

Some Important Issues Regarding LinTrans (optional)

Explanation of the issues. For more information see Nil and [some other help files].

Creation / Class Methods

*new (matrix)

Short prose description of method.

matrix - Explanation of matrix. Default value is nil. Other information.

g = LinTrans(Matrix.with([[1,2],[2,3]]));

*rotation2D (theta)

2D rotation linear transformation for angle theta.

a = LinTrans.rotation2D(pi/2);

a.value(RealVector[1,0])

Accessing Instance and Class Variables

matrix_(arg1)

matrix

the matrix that represents the transformation.

*

Linear transformation and scalar multiplication.

a = LinTrans(Matrix.with([[1,2],[3,4]]));

b = LinTrans(Matrix.with([[3,4],[5,6]]));

(a*b).value(RealVector[5,6])

a = LinTrans.rotation2D(pi/2);

b = LinTrans.rotation2D(pi/2);

(a*b).value(RealVector[1,0]) //rotate vector by pi

+

addition between linear transformations.

a = LinTrans(Matrix.with([[1,2],[3,4]]));

b = LinTrans(Matrix.with([[3,4],[5,6]]));

(a+b).value(RealVector[5,6])

-

subtraciton between linear transformations.

a = LinTrans(Matrix.with([[1,2],[3,4]]));

b = LinTrans(Matrix.with([[3,4],[5,6]]));

(a-b).value(RealVector[5,6])

det

determinant of the transformation.

LinTrans(Matrix.with([[1,2],[2,3]])).det

inverse

inverse transformation.

a = LinTrans(Matrix.with([[1,2],[2,3]]));

b = a.inverse;

(a*b).value(RealVector[1,2]) //a*b is identity