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## Main Question or Discussion Point

Hi,

I'm reading Shilov's linear algebra and in part 2.44 he talks about linear independent vectors in a subspace L which is a subset of space K( he refers to it as K over L). I don't understand why he says that a linear combination of vectors of the subspace L and vectors of the subspace K over L is independent. Is it the same subspace or am I wrong? Shilov also says that the dimension of the subspace K over L n-l. Why?

LINK to the page:

http://books.google.com.mx/books?id=5U6loPxlvQkC&pg=PA44&lpg=PA44&dq=2.44+shilov+linear+algebra&source=bl&ots=bcYpdoyvx7&sig=3daYGhPuQKVDbO2nc1TGrXb75tA&hl=es&sa=X&ei=P1MaU9nrOYPj2AWKjYHQCw&ved=0CEkQ6AEwAw#v=onepage&q=2.44%20shilov%20linear%20algebra&f=false

I'm reading Shilov's linear algebra and in part 2.44 he talks about linear independent vectors in a subspace L which is a subset of space K( he refers to it as K over L). I don't understand why he says that a linear combination of vectors of the subspace L and vectors of the subspace K over L is independent. Is it the same subspace or am I wrong? Shilov also says that the dimension of the subspace K over L n-l. Why?

LINK to the page:

http://books.google.com.mx/books?id=5U6loPxlvQkC&pg=PA44&lpg=PA44&dq=2.44+shilov+linear+algebra&source=bl&ots=bcYpdoyvx7&sig=3daYGhPuQKVDbO2nc1TGrXb75tA&hl=es&sa=X&ei=P1MaU9nrOYPj2AWKjYHQCw&ved=0CEkQ6AEwAw#v=onepage&q=2.44%20shilov%20linear%20algebra&f=false