The inner product axioms are the following:(adsbygoogle = window.adsbygoogle || []).push({});

##\text{(a)} \ \langle x+z,y \rangle = \langle x,y \rangle + \langle z,y \rangle##

##\text{(b)} \ \langle cx,y \rangle = c\langle x,y \rangle##

##\text{(c)} \ \overline{\langle x,y \rangle} = \langle y,x \rangle##

##\text{(d)} \ \langle x,x \rangle > 0 \ \text{if} \ x \ne 0##

What about these axioms imply that ##\langle x,y \rangle \ge 0## for all ##x## and ##y##?

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# I Non-negativity of the inner product

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