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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?
 one year ago
 one year ago
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?
 one year ago
 one year ago

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fatemeh8989Best ResponseYou've already chosen the best response.1
basis is a set of vectors which 1. all of members are linearly independent and 2. all combinations of members can produce space.
 one year ago

fatemeh8989Best ResponseYou've already chosen the best response.1
any question about this?
 one year ago

fatemeh8989Best ResponseYou've already chosen the best response.1
the dimension of a space is the cardinal of basis set.
 one year ago

littlecatBest ResponseYou've already chosen the best response.0
what is the "cardinal"? were my first two statements accurate?
 one year ago

fatemeh8989Best ResponseYou've already chosen the best response.1
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.
 one year ago

fatemeh8989Best ResponseYou've already chosen the best response.1
and also....the matrix that u mentioned in ur statement should have some conditions... that fullfil this, you know them?
 one year ago

littlecatBest ResponseYou've already chosen the best response.0
the columns should be independent?
 one year ago

fatemeh8989Best ResponseYou've already chosen the best response.1
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?
 one year ago

fatemeh8989Best ResponseYou've already chosen the best response.1
welcome :) good luck :)
 one year ago
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