## Subsection11.1.3What 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.