- #1
Mr Davis 97
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The inner product axioms are the following:
##\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##?
##\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##?