Numerical Linear Algebra. Neuman Lemma.

Prove the Neuman Lemma: if ||A|| < 1, then I - A is invertible. Here ||.|| is a norm on the space of nxn matrices induced by a norm on R^n or C^n ( C is complex plane). I want a detailed proof. Thanks.

Subspace of inner product. Numerical Linear Algebra.

Please help with problem # 1 of this set. Thanks. (See attached file for full problem description)

Numerical Linear algebra. Orthogonal matrix.

Please help with problem 6 of this set. Don't need to describe the action of Q on R^2. (See attached file for full problem description)

Numerical Linear Algebra. Orthogonal matrix/eigenvalues.

Let A be a 3 x 3 real orthogonal matrix with det A = 1. Prove that lambda = 1 is an eigenvalue of A.

Numerical Linear algebra. Gram-Schmidt orthogonalization.

Please help with problem 5 to obtain orthogonal basis. Don't worry about the extra credit part. (See attached file for full problem description)

Numerical Linear algebra. Gram-Schmidt orthogonalization.

See attached file for full problem description.

Numerical Linear algebra. Vector spaces. Inner products.

Let V be the vector space of all complex valued polynomials defined over the half line [0,infinity). (a) Show that = integral from 0 to infinity of f(x) ( g(x) bar) e^-x dx is a complex inner product on V g(x) bar is g(x) with a bar on it, which I believe to be the conjugate. (b) Find an orthonormal set ...continues

Investment, Time Value of Money, Etc.

Old Alfred Road, who is well-known to drivers on the Maine Turnpike, has reached his seventieth birthday and is ready to retire. Mr. Road has no formal training in finance but has saved his money and invested carefully. Mr. Road owns his home-the mortgage is paid off-and does not want to move. He is a widower, and he wants to b ...continues

Budget

Overview River Beverages is a food and soft-drink company with worldwide operations. The company is organized into five regional divisions with each vice president reporting directly to the CEO, Cindy Wilkins. Each vice president has an R&D department, controller, and three divisions; carbonated drinks, juices and water, and f ...continues

Matlab project. Numerical Linear Algebra.

Please see the attached file. This is for a Numerical Linear Algebra class. I was trying to modify the matlab built-in lutx function, by using for loops, but when I tested the results with my new function it didn't give the same results. I am still hoping that someone can help me. :(