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Transformation Matrix

Main Concept

A linear transformation on a vector space is an operation T on the vector space satisfying two rules:

 

Tx+y=Tx+Ty,

Tα x=α Tx

for all vectors x, y, and all scalars α.

 

Any linear transformation T in the Euclidean plane is characterized by the action of that transformation on the standard basis:

 

Tx = Tx1i+x2 j=x1Ti+x2Tj

 

=A . x

where

A=TiTj,   x = x1x2,   i=10,    j=01.

 

The matrix A, whose columns are the transformed basis vectors, is known as the transformation matrix associated to the transformation T.

Click and/or drag on the graph to change the initial vector x or the transformation vectors Ai and Aj. You can also edit the values of the transformation matrix A and the vector x directly.

A

x

=

Ax

=

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