1. ## Inner product space

Show that in an inner product space, x perpendicular to y if and only if $\displaystyle ||x+\alpha y||\geqslant||x||$ for all sclar $\displaystyle \alpha$

2. For example, if the inner product space is real, express the inequality in the form $\displaystyle \alpha(2<x,y>+\alpha||y||^2)\geq 0$ .

3. Originally Posted by geezeela
Show that in an inner product space, x perpendicular to y if and only if $\displaystyle ||x+\alpha y||\geqslant||x||$ for all sclar $\displaystyle \alpha$
Sorry i meant to say
Show that in an inner product space, x orthogonal to y if and only if $\displaystyle ||x+\alpha y||\geqslant||x||$ for all sclar $\displaystyle \alpha$

4. Originally Posted by geezeela
Sorry i meant to say Show that in an inner product space, x orthogonal to y if and only if $\displaystyle ||x+\alpha y||\geqslant||x||$ for all sclar $\displaystyle \alpha$

Many thanks for this information.

5. ## Re: Inner product space

I need some help with this question...please guys help me....

6. ## Re: Inner product space

Originally Posted by geezeela
I need some help with this question...please guys help me....
What about the hint I gave you?