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Let V be a finite-dimensional vector space over C with dimension n. Prove that if V is
Chapter 1, Problem 28(choose chapter or problem)
QUESTION:
Let V be a finite-dimensional vector space over C with dimension n. Prove that if V is now regarded as a vector space over R, then dim V = 2n. (See Examples 11 and 12.)
Questions & Answers
QUESTION:
Let V be a finite-dimensional vector space over C with dimension n. Prove that if V is now regarded as a vector space over R, then dim V = 2n. (See Examples 11 and 12.)
ANSWER:Step 1 of 3
Let us consider a finite dimensional vector space over with dimension .
As is a vector space over the field of with dimension , the basis for has linearly independent vectors.