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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

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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.)

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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.

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