- #1

Amadeo

- 28

- 9

- Homework Statement
- Let a1, a2, a3 be linearly independent vectors in R 3 , and let q1, q2, q3 be the vectors obtained from a1, a2, a3 by the Gram-Schmidt algorithm.

Define the linear transformation T : R 3 → R 3 by T(q1) = a1, T(q2) = a2 and T(q3) = a3.

For the choice of basis {q1, q2, q3} both for the input and output spaces, find the matrix MT which represents the linear transformation T for this choice of basis.

- Relevant Equations
- projection equation used in Gram-Schmidt: p=((a^t)(b))/((a^t)(a)) (a)

My idea was to write out the formulas for the orthogonal q vectors in terms of the input vectors using the basics of gram-schmidt. Then, I would rewrite those equations suhc that the a vectors were written in terms of the q vectors. And then, try to find some matrix which would capture the needed transformation. However, the q vectors must be written in terms of multiple a vectors, as well as other q vectors. Additionally, the need to make all of the orthogonal vecotrs of unit length makes it even more complicated. There must be another way.