- #1
franz32
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Hello everyone! =)
This might be a good challenge to everyone here... =)
1.) Let A be an n X n matrix and let x and y be vectors in R^n.
Show that Ax .y = x.(A^T)(y), where "." means dot product and T is 'transpose'.
2. show that u.v = (1/4)// u + v //^2 - (1/4)//u - v//^2
where u and v are vectors; "." means dot product and
//...// denote the length of a vector.
3. Prove the parallelogram law: // u + v //^2 + // u - v //^2 =
2 //u//^2 + 2 //v//^2.
4. Prove the Vandermonde determinant.
This might be a good challenge to everyone here... =)
1.) Let A be an n X n matrix and let x and y be vectors in R^n.
Show that Ax .y = x.(A^T)(y), where "." means dot product and T is 'transpose'.
2. show that u.v = (1/4)// u + v //^2 - (1/4)//u - v//^2
where u and v are vectors; "." means dot product and
//...// denote the length of a vector.
3. Prove the parallelogram law: // u + v //^2 + // u - v //^2 =
2 //u//^2 + 2 //v//^2.
4. Prove the Vandermonde determinant.
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