Let L:V→W be a linear transformation. Explain the meaning of the following statement: The action...
Let be a linear transformation. Explain the
meaning of the following statement:
The action of the linear transformation L is
completely determined by its action on a basis
Answer & Explanation
Skilled2021-10-26Added 93 answers
is a linear transformation.
Now, if is a basis for V such that:
, for all i,
Then, the action of L on any element of V can be determined.
Let v be in V.
Therefore, L(v) is determined.
Thus, “the action of L is completely determined by its action on a basis for V”.
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