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I'm in the process of reading my first Linear Algebra textbook, and was just wondering...Is the standard basis of a vector space in n dimensions equivalent to the row space of the n x n identity matrix?

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    Yeah, I phrased the question wrong; that is what I wanted to know though. As I said, I'm in the process of learning Linear Algebra for the first time and just wanted to make sure that I understood the idea of a "standard basis". Thanks!2011-01-27

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I assume you're talking about $\mathbb{R}^n$? First off, the standard basis $\{e_1,e_2,\dots,e_n\}$ is a linearly independent set of $n$ vectors, which spans the vector space.

However, the row space of $I_n$ is the set of all linear combinations of the row vectors, which gives a subspace of $n$-dimensional space, which is just the whole space in this case.

The key difference is that the standard basis is just a set of basis vectors, but the row space of $I_n$ is a vector space, not a standard basis, which are two different objects.

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    @user6300 Ah, my mistake that I didn't answer your intended question. Thankfully Arturo has better explained it to that end.2011-01-27