[Eeglablist] QR factorization and SVD for XDAWN algorithm

Mon Jan 23 07:29:59 PST 2017

Greetings,

This is my first post and in this post I want to clarify if I am going
in the right direction while trying to understand the concept of QR
factorization for xDAWN algorithm

So here is what I have found and understood

QR factorization is primary to full rank the least square problems. Full
rank of a matrix is the full row (column) rank when each of the rows
(columns) of the matrix are linearly independent. We need the
row(column) to be linearly independent so that the vectors in the matrix
are linearly independent.

This is related to eigen values and eigen vectors where in-order to say
something about the dimensionality of the space spanned by the eigen
vectors, it is important to tell when the eigen vectors are linearly
independent.

Now why do we need to find the dimensionality of the space spanned by
the eigen vectors, this can be explained by saying if we know the space
spanned by the eigen vector, we know the largest eigen value which is
responsible for it.

These large eigen value are obtained by singular value decomposition in
the form of diagonal matrix.

As you might have noticed that I am just interested in the theory and
how this theory works and why it is been considered. So if you feel that
my understanding is inaccurate, please feel free to clarify.

Best Regards,