Dear members,

I have a matrix with a pattern, it starts from an index given by a value for the integers, i.e, i=0, 1, 2,3.... As I know the matrix which multiplies a vector of data (also with defined values based on special constants), which alternative coming from the known techniques of linear algebra lets operate on the rows in order to transform the original matrix to its inverse? (Is still valid the Gauss reduction techniques or others modern?) Not sure if an inverse matrix with infinite elements could be gotten easily, as theoretically the definition of square matrix does not apply or we need to imagine an infinite square matrix (infinite rows and columns as in M, below).

I know the old methods, but the modern algebra or formal lets define properly the operations for a matrix like this, from which I need get its inverse:

M= ( ( 1 0 0 0 .... 0....) for i=0

(1 2 4 8.... (2 at j).... ) for i=1

(1 2x2 (2 at 4) (2 at 6) ...... ) for i=2

(1 2x3 (( 2 at 2) X (3 at 2)) (2 at 3( x (3 at 3)...... ) for i=3

....

....

..... );

In general, I pursuit for methods to determine properly the inverse of this matrix or for all kind of matrices, if applies. the matrix M lets calculate some terms involving the Bernoulli numbers from a special coefficients G0, G1, G2, .... which I need to define thanks to the inverse. Inverse might be possible.

Thanks

Carlos