一道有关线性代数的题目(题目是用英语出的)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|=||
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![一道有关线性代数的题目(题目是用英语出的)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|=||](/uploads/image/z/10397415-39-5.jpg?t=%E4%B8%80%E9%81%93%E6%9C%89%E5%85%B3%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E7%9A%84%E9%A2%98%E7%9B%AE%EF%BC%88%E9%A2%98%E7%9B%AE%E6%98%AF%E7%94%A8%E8%8B%B1%E8%AF%AD%E5%87%BA%E7%9A%84%EF%BC%89For+the+vectors+v%3D%283%2C4%29+and+w%3D%283%2C4%29+test+the+Schwarz+inequality+on+v%C2%B7w+and+the+triangle+inequality+on+%7C%7Cv%2Bw%7C%7C.Find+cosA+for+the+angle+between+v+and+w.When+will+we+have+equality+%7Cv%C2%B7w%7C%3D%7C%7C)
一道有关线性代数的题目(题目是用英语出的)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|=||
一道有关线性代数的题目(题目是用英语出的)
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||?
一道有关线性代数的题目(题目是用英语出的)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|=||
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||