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I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ...
I am currently reading Chapter 12: Multilinear Algebra and am specifically focused on Section 12.1: Vectors and Tensors ...
I need help in fully understanding Corollary 12.4 to Theorem 12.2 ... ...
Theorem 12.2 and its corollaries read as follows:
View attachment 8795
View attachment 8796In the above text from Browder, we read the following:
" ... ... 12.4 Corollary. If $$x \in V$$, and $$x \neq 0$$, there exists $$\alpha \in V^*$$ such that $$\alpha (x) \neq 0$$ ... ... "
Can someone please demonstrate a formal and rigorous proof for Corollary 12.4 ...?
Help will be appreciated ... ...
Peter
I am currently reading Chapter 12: Multilinear Algebra and am specifically focused on Section 12.1: Vectors and Tensors ...
I need help in fully understanding Corollary 12.4 to Theorem 12.2 ... ...
Theorem 12.2 and its corollaries read as follows:
View attachment 8795
View attachment 8796In the above text from Browder, we read the following:
" ... ... 12.4 Corollary. If $$x \in V$$, and $$x \neq 0$$, there exists $$\alpha \in V^*$$ such that $$\alpha (x) \neq 0$$ ... ... "
Can someone please demonstrate a formal and rigorous proof for Corollary 12.4 ...?
Help will be appreciated ... ...
Peter