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Subsection 11.1.3 What you will learn

This week, you finally discover practical algorithms for computing the Signgular Value Decomposition.

Upon completion of this week, you should be able to

  • Link the (Reduced) SIngular Value Decomposition of \(A \) to the Spectral Decomposition of \(A^H A \text{.}\)

  • Reduce a matrix to bidiagonal form.

  • Transform the implicitly shifted QR algorithm into the implicitly shifted bidiagonal QR algorithm.

  • Use Jacobi rotations to propose alternative algorithms, known as Jacobi's Methods, for computing the Spectral Decomposition of a symmetric matrix and Singular Value Decomposition of a general real-valued matrix.