Question

Is this right?

The dimension of the space spanned by a matrix is the number of columns of the matrix.

The dimension of a matrix is the number of rows of a matrix. The matrix exists in R^m, where m is the number of rows.

Can someone give a clear definition of basis, span, and dimensions?

Answer 1

basis is a set of vectors which 1. all of members are linearly independent
and 2. all combinations of members can produce space.

Answer 2

any question about this?

Answer 3

the dimension of a space is the cardinal of basis set.

Answer 4

what is the "cardinal"?

were my first two statements accurate?

Answer 5

cardinal is the number of members of a set. your statements are not wrong... but hard to have an imagination in mind. at least for me. ( :d ) . by the definition i gave above. you can easily find out what you have to be looking for. or actually what a basis is.

Answer 6

and also....the matrix that u mentioned in ur statement should have some conditions... that fullfil this, you know them?

Answer 7

the columns should be independent?

Answer 8

exactly...!!! which is condition 1 in basis definition.
and second condition in definition produce the space of your matrix. but generally if the space be whatever... any vectors ( even objects) the importance of condition 2 becomes more clear. i hope i didn't confused you. need more explanation?

Answer 9

Thanks!

Answer 10

welcome :) good luck :)