UC知道一道有关线性代数的题目（题目是用英语出的）
来源：百度知道 编辑：UC知道 时间：2024/05/29 14:28:16
For the vectors v=(3,4) and w=(3,4) test the Schwarz inequality on v·w and the triangle inequality on ||v+w||.
Find cosA for the angle between v and w.
When will we have equality |v·w|=||v|| ||w|| and ||v+w||=||v||+||w||?
Find cosA for the angle between v and w.
When will we have equality |v·w|=||v|| ||w|| and ||v+w||=||v||+||w||?
1、Schwarz不等式是|v·w|≤||v||×||w||
||v||＝5，||w||＝5，v·w＝25，所以，|v·w|＝25＝||v||×||w||，满足Schwarz不等式.
三角不等式：||v＋w||≤||v||＋||w||
v＋w＝(6,8)，||v＋w||＝10，所以||v＋w||＝10＝||v||＋||w||，满足三角不等式.
2、v与w的夹角的余弦cosA＝(v·w)/(||v||×||w||)＝25/(5×5)＝1
3、当且仅当|cosA|＝1，即A＝0或π时， |v·w|＝||v||×||w||
当且仅当cosA＝1，即A＝0时，||v＋w||＝||v||＋||w||