A linear transformation on a vector space is an operation T on the vector space satisfying two rules:
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→
A=Ti∧Tj∧, 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 A⋅i∧ and A⋅j∧. You can also edit the values of the transformation matrix A and the vector x→ directly.
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