作业帮Linear MappingLet V be an n dimensional vector space with basis B.Let S be the vector space of all linear operators L: V->V.Define T: S->M(n,n) by T(L)=[L]_B.Prove that T is linear.只有英语的.小弟不知道中文怎么说.各位大神,这道题
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![Linear MappingLet V be an n dimensional vector space with basis B.Let S be the vector space of all linear operators L: V->V.Define T: S->M(n,n) by T(L)=[L]_B.Prove that T is linear.只有英语的.小弟不知道中文怎么说.各位大神,这道题](/uploads/image/z/11669418-18-8.jpg?t=Linear+MappingLet+V+be+an+n+dimensional+vector+space+with+basis+B.Let+S+be+the+vector+space+of+all+linear+operators+L%3A+V-%3EV.Define+T%3A+S-%3EM%28n%2Cn%29+by+T%28L%29%3D%5BL%5D_B.Prove+that+T+is+linear.%E5%8F%AA%E6%9C%89%E8%8B%B1%E8%AF%AD%E7%9A%84.%E5%B0%8F%E5%BC%9F%E4%B8%8D%E7%9F%A5%E9%81%93%E4%B8%AD%E6%96%87%E6%80%8E%E4%B9%88%E8%AF%B4.%E5%90%84%E4%BD%8D%E5%A4%A7%E7%A5%9E%2C%E8%BF%99%E9%81%93%E9%A2%98)
Linear MappingLet V be an n dimensional vector space with basis B.Let S be the vector space of all linear operators L: V->V.Define T: S->M(n,n) by T(L)=[L]_B.Prove that T is linear.只有英语的.小弟不知道中文怎么说.各位大神,这道题
Linear Mapping
Let V be an n dimensional vector space with basis B.
Let S be the vector space of all linear operators L: V->V.
Define T: S->M(n,n) by T(L)=[L]_B.
Prove that T is linear.
只有英语的.小弟不知道中文怎么说.
各位大神,这道题怎么做?中文英文都可以.
给各思路也行.
谢谢了!
Linear MappingLet V be an n dimensional vector space with basis B.Let S be the vector space of all linear operators L: V->V.Define T: S->M(n,n) by T(L)=[L]_B.Prove that T is linear.只有英语的.小弟不知道中文怎么说.各位大神,这道题
我想[L]_B表示线性变换L在基B下的矩阵吧
任取L1,L2∈S,k≠0
T(L1+L2)=[L1+L2]_B=[L1]_B+[L2]_B
T(kL1)=[kL1]_B=k[L1]_B
所以T是线性的
高等代数的！！
我看懂了题目！却忘了大学的高代！！！！
帮不了你了！！
给题目的大概翻译给你
设V 是具有基 B的一个 n 维向量空间 。设 S 是向量空间的所有线性算子 L:v-V. 定义 T：S->M(n,n) ，其中 T(L)=[L]_B 。证明：T是线性的。