[Eeglablist] QR factorization and SVD for XDAWN algorithm

[Guruprasad Madhale Jadav]

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,
Guruprasad Madhale Jadav