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courtrigrad
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Hello all
Show that the equality signs in Schwarz's Inequality holds if, and only if, the a's and b's are proportional; that is; [tex] ca_{v} + db_{v} = 0 [/tex] for all v's where c and d are independent of v and not both zero. How would I even begin this? I know Schwarz's Inequality is:
[tex] (a_1b_1 + a_2b_2 + ... + a_nb_n)^2 \leq (a_1^2 +... + a_n^2)(b_1^2 + ...+ b_n^2) [/tex] Now we need to show that the equality sign holds given the above conditions.
Would i use the fact of direct proportionality, [tex] y = kx [/tex]?
Thanks
Show that the equality signs in Schwarz's Inequality holds if, and only if, the a's and b's are proportional; that is; [tex] ca_{v} + db_{v} = 0 [/tex] for all v's where c and d are independent of v and not both zero. How would I even begin this? I know Schwarz's Inequality is:
[tex] (a_1b_1 + a_2b_2 + ... + a_nb_n)^2 \leq (a_1^2 +... + a_n^2)(b_1^2 + ...+ b_n^2) [/tex] Now we need to show that the equality sign holds given the above conditions.
Would i use the fact of direct proportionality, [tex] y = kx [/tex]?
Thanks
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