Re: [線代] maxium norm
※ 引述《asdc20 (asdc20)》之銘言:
: Prove the following inequality used in verifying the maximum norm for
: R3.
: max{|x1|+|y1|,|x2|+|y2|,|x3|+|y3|} <= max{|x1|,|x2|,|x3|}+max{|y1|,|y2|,|y3|}
: 先謝謝各位的回覆......
Let |xj|+|yj| be the largest number of the left hand side.
Since |xj| <= max{|x1|,|x2|,|x3|} and |yj| <= max{|y1|,|y2|,|y3|},
we have |xj|+|yj| <= max{|x1|,|x2|,|x3|}+max{|y1|,|y2|,|y3|}.
This completes the proof.
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