Is the svd of a given matrix a unique in general

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1. (a) Suppose that A is an orthogonal matrix. What are its singular values?

(b) Is the SVD of a given matrix A unique in general?

2. Obtain the matrix A for Example 4.17 in the case where v'(0) = v'(1) = 0, and show that it is singular.

Example 4.17

(differential equations). Consider the recovery of a function v(t) from its given second derivative -g(t) on the interval [0,1]. Such a problem is typical for many applications. An example is the celebrated heat equation in one dimension: if the intensity of a heat source is given and we wish to recover the steady-state temperature of the body that is being heated, then under certain simplifying assumptions about the heat conductivity properties of the material we obtain a problem of the same type.

Reference no: EM131263607

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