A linear transformation on a vector space is an operation on the vector space satisfying two rules:
for all vectors , , and all scalars .
Any linear transformation in the Euclidean plane is characterized by the action of that transformation on the standard basis:
, , , .
The matrix , whose columns are the transformed basis vectors, is known as the transformation matrix associated to the transformation .
Click and/or drag on the graph to change the initial vector or the transformation vectors A and A. You can also edit the values of the transformation matrix A and the vector directly.
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