Here are the MAPLE procedures that solve this assignment.

In the first file Gauss_Elim-final we solve the Gaussian elimination problem of the Hilbert matrices.

The main procedure there is the algorithm you supplied, so I didn't comment in the procedure itself.

The file LU-final solves the Doolittle LU decomposition problem.

Since the Doolittle algorithm results in an upper ...

Solution Summary

This shows how to work with Hilbert matrices to solve a system of equations using Gaussian elimination and to find the Doolittle LU decomposition with scaled partial pivoting.

... Let V=L2[-1,1] be the Hilbert space of functions ... of the scalar product, the elements of the matrix providing the ... which in terms of matrices is x MT y = (T ax ...

... rotation D(theta) that acts on the 2 dimensional Hilbert space. So, D(theta) will be a 2 by 2 matrix. ... of the algebra of the 3 by 3 rotation matrices in terms ...

In the Hilbert space C^2 x C^2 (where x is used in all of my notation to mean the ... (NOTE: where q_3 is sigm_3, X is tensor product, I is identity matrix, and we ...

... verifying that the result is the identity matrix (I have done myself this and other checks of the numerical values). Linear Transformations, Hilbert Space and ...

... all the | sn 's. But if they form a complete set, they span the entire Hilbert space. ... In a matrix representation we can deﬁne the n-th unit vector to be | sn ...

... A is Hermitian A_{i,j} = A_{j,i}*, so this also fixes all the other matrix elements. ... we describe the state of a system by a vector in a so-called Hilbert space ...

...Hilbert said the term zahlring [number ring] for sets of this ... n ( R ) be the ring of nxn matrices with entries ... ϕ : R → S , taking r ∈ R to the nxn matrix. ...

C) The famous Hubert matrices are given by Hij= 1/(i +j - 1). The nxn Hilbert matrix Hn is easily produced in MATLAB using hilb(n). Assume the true solution of ...