- #1
SprucerMoose
- 62
- 0
G'day,
I'm doing some questions on whether or not a given set spans a given vector space and was wondering what the best way to write out a matrix is.
For example, if I am wanting to show that a bunch of M2X2 elements spans M2X2, can I express each matrix as a coordinate vector with respect to a basis say B={Ei,j|i=1,2;j=1,2}.
I have been writing my sets along the lines of...
SB = {(1,2,3,4), (2,3,4,5),...}
to make it easier to write, but I'm not sure if this is the correct notation. Is is acceptable rewrite the whole set with respect to a basis like this? What is the best way to resolve matrices into a simpler form for calculation in such a scenario?
Also, in the general case, if I represent a bunch of vectors with respect to some other basis, if these vectors are linearly independent and/or span a subspace in the new basis, does that imply that, with respect to the original basis, the vectors span the same subspace and are also independent?
Thanks
I'm doing some questions on whether or not a given set spans a given vector space and was wondering what the best way to write out a matrix is.
For example, if I am wanting to show that a bunch of M2X2 elements spans M2X2, can I express each matrix as a coordinate vector with respect to a basis say B={Ei,j|i=1,2;j=1,2}.
I have been writing my sets along the lines of...
SB = {(1,2,3,4), (2,3,4,5),...}
to make it easier to write, but I'm not sure if this is the correct notation. Is is acceptable rewrite the whole set with respect to a basis like this? What is the best way to resolve matrices into a simpler form for calculation in such a scenario?
Also, in the general case, if I represent a bunch of vectors with respect to some other basis, if these vectors are linearly independent and/or span a subspace in the new basis, does that imply that, with respect to the original basis, the vectors span the same subspace and are also independent?
Thanks
Last edited: