A geographic example may help to clarify the concept of linear independence.
2.
I don't think that this is a sufficient condition to ensure linear independence.
3.
Matrix methods are significantly limited for MIMO systems where linear independence cannot be assured in the relationship between inputs and outputs.
4.
In the base space, this linear independence manifests as each point lying outside the object defined by the other points.
5.
The linear independence of the columns of a generator matrix of an MDS code permits a construction of MDS codes from objects in finite projective geometry.
6.
So, to get linear independence all non zero m-tuples with one as a top most non zero element will be chosen as columns.
7.
Clearly, any block-diagonal matrices constructed from involutory matrices will also be involutory, as a consequence of the linear independence of the blocks.
8.
If 0 } }, then the previous theorem implies that would be in the-span of, contradicting the-linear independence of, therefore.
9.
By the Gram Schmidt process, it is the same to ask for ( pointwise ) linear independence or fields that give an orthonormal basis at each point.
10.
It certainly satisfies the properties mentioned in the introduction to wedge product to do with linear independence .-- talk ) 15 : 22, 29 March 2008 ( UTC)
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