My text is not helping at all and the wikipedia explanations of the concepts: basis and dimension are way over my head.

Let V be the space of polynomials in x and y of degree <= 10. Specify a basis of V and compute dimV.

thanks

jblorien

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- Mar 15th 2008, 08:13 AMjblorienDimension and basis
My text is not helping at all and the wikipedia explanations of the concepts: basis and dimension are way over my head.

Let V be the space of polynomials in x and y of degree <= 10. Specify a basis of V and compute dimV.

thanks

jblorien - Mar 15th 2008, 09:17 AMgalactus
To be a basis it must span and be linearly independent.

The polynomials span the vector

space of since each p in can be

written as which is a

linear combination of .

. The basis has n+1 vectors. In other words, it has dimension 11.