LetFbe the linear transformation that switches for and vice versa. Find the transformation matrixAfor this linear transformation.

Then find the vectors so that and . Choose this as a basis, and then find F's transformation matrix in this basis.

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- Apr 10th 2009, 09:14 AMSpec[SOLVED] Linear transformation
Let

**F**be the linear transformation that switches for and vice versa. Find the transformation matrix**A**for this linear transformation.

Then find the vectors so that and . Choose this as a basis, and then find F's transformation matrix in this basis. - Apr 10th 2009, 10:18 AMNonCommAlg
so we have and which gives you hence

Quote:

Then find the vectors so that and . Choose this as a basis, and then find F's transformation matrix in this basis.

the matrix of F in this new basis is obviously:

remember: if then would be the j-th column of the matrix of F with respect to the basis - Apr 10th 2009, 10:58 AMSpec
- Apr 10th 2009, 11:26 AMNonCommAlg