MHB Understanding Orthogonality in Inner Product Spaces

[mathmari]

Hey!

We know that:
$$(x,x)=0 \Rightarrow x=0$$

When we have $\displaystyle{(x,y)=0}$, do we conclude that $\displaystyle{x=0 \text{ AND } y=0}$. Or is this wrong? (Wondering)

 

[I like Serena]

Hey!

We know that:
$$(x,x)=0 \Rightarrow x=0$$

When we have $\displaystyle{(x,y)=0}$, do we conclude that $\displaystyle{x=0 \text{ AND } y=0}$. Or is this wrong? (Wondering)

Hi hi! (Happy)

In this case we can only say that $x$ and $y$ are perpendicular, or one of them is zero.
Note that $(\hat \imath, \hat \jmath) = 0$. (Wasntme)

 

[mathmari]

Hi hi! (Happy)

In this case we can only say that $x$ and $y$ are perpendicular, or one of them is zero.
Note that $(\hat \imath, \hat \jmath) = 0$. (Wasntme)

I see! Thanks a lot! (Sun)