Recent content by Abuattallah

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    Graduate Finding Dual Basis of Linear Functionals for a Given Basis in C^3

    Hello, Problem, let B={a_1,a_2,a_3} be a basis for C^3 defined by a_1=(1,0,-1) a_2=(1,1,1) a_3=(2,2,0) Find the dual basis of B. My Solution. Let W_1 be the subspace generated by a_2=(1,1,1) a_3=(2,2,0), let's find W*, where W* is the set of linear anihilator of W_1. Consider the system...
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    Graduate Linear Operator T on Vector Space V: Unique Matrix A in Ordered Bases B

    Thank you so much Tiny-Tim. and thanks for word correction, English is my second language ; ). You have all a wonderful day, Abuattallah
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    Graduate Linear Operator T on Vector Space V: Unique Matrix A in Ordered Bases B

    Thank you tiny-tim. This is my try: consider the base B'={a,Sa,...,S^{n-1}a}, for some a where S^ia≠0, \forall i≤n-1, now for the sake of simplicity let's call them as follow a=a_1, Sa=a_2,...,S^ia=a_{i+1},...,S^{n-1}=a_n,Consider the follwing c_1a_1+...+c_na_n=0 ... (1) Aplly S^{n-1} to...
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    Graduate Linear Operator T on Vector Space V: Unique Matrix A in Ordered Bases B

    Hello, I am a grad student preparing for a quals. I am using H. and Kunze book. the problem is: let V be a n-dim vector space over F. and let B={a_1,a_2,..., a_n} be an ordered bases for V. a- According to them 1, there is a unique Linear operator T on V such that Ta_i=a_{(i+1)} ...