Question

PLease urgent help me.(Singular Value Decomposition-MATLAB)

THE SVD THEOREM Develop a one line MATLAB command to compute Σ-1 that only uses the function d i a g.

Answer 1

Answer:)

We know that $\mathbf{\tilde{\Sigma}}$ is a diagonal matrix, with all non-zero entries being the norm of the eigenvalues of the matrix $\mathbf{A}$. Let these diagonal values be denoted be $\lambda_i$, where none of these are zero in value.

Then, we can denote the $\mathbf{\tilde{\Sigma}}$ matrix as given in the question, with $\mathbf{{\Sigma}}$ being a block matrix containing all the $\lambda_i$ on it's main diagonal.

Now, the inverse for $\mathbf{\tilde{\Sigma}}$ , denoted by $\mathbf{\tilde{\Sigma}}^{-1}$ , is just the matrix with the diagonal values inverse, that is

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This, in MATLAB is given by the following:

• Define an array of the $\Sigma$ values as values = [lambda_1, lambda_2, lambda_3, ... , lambda_N]
• Then the required inverse is diag(values.^(-1),N,N), where N is the number of such diagonal values which are non-zero.