Monday

September 1, 2014

September 1, 2014

Posted by **Traxx** on Sunday, January 2, 2011 at 11:04am.

- Linear Algebra -
**Marth**, Sunday, January 2, 2011 at 11:12amDefine proj(u, v) to be the projection of u onto v. proj(u, v) = v*(u dot v)/(v dot v)

||u|| = norm u

From the 3 given vectors, we want to form a basis such that each basis vector is orthogonal to every other and an unit vector.

Take e1 = ||[1,0,1]|| = (1/sqrt(2))[1,0,1]. The first basis vector is arbitrary.

e2 = ||[0,1,2] - proj([0,1,2], [1,0,1])||. We remove the non-orthogonal part to ensure e2 is orthogonal. Then take the norm to make it an unit vector.

e3 = ||[2,1,0] - proj([2,1,0], [0,1,2]) - proj([2,1,0], [1,0,1])||. As with e2, remove every part orthogonal to e1 or e2 to ensure orthogonality. Then take the norm to make it an unit vector.

**Related Questions**

math - A trigonmetric polynomial of order n is t(x) = c0 + c1 * cos x + c2 * cos...

math - Find an orthonormal basis for the subspace of R^3 consisting of all ...

math - Find the least squares approximation of x over the interval [0,1] by a ...

Math - 1. P5 is an innerproduct space with an inner product. We applied the ...

accounting - With this being 450.00 from Dec 31, 2003 to Dec, 31 2006 what would...

ACC 225 - What is the difference between cash basis and accrual basis accounting...

Accounting - What is the difference between cash basis and accrual basis ...

calculus - P2 has a mysterious inner product * for which {x+4, 3x-5} is an ...

calculus - P2 has a mysterious inner product * for which {x+4, 3x-5} is an ...

linear algebra - what is the basis of a subspace or R3 defined by the equation ...