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Exercise 2

Avg difficulty 2.5

Find singular value decompositions for the following matrices:

  1. [000−8]\begin{bmatrix} 0 & 0 \\ 0 & -8 \end{bmatrix}.

  2. [2302]\begin{bmatrix} 2 & 3 \\ 0 & 2 \end{bmatrix}.

  3. [400002]\begin{bmatrix} 4 & 0 & 0 \\ 0 & 0 & 2 \end{bmatrix}

  4. [400002]\begin{bmatrix} 4 & 0 \\ 0 & 0 \\ 0 & 2 \end{bmatrix}

Austin, Understanding Linear Algebra, §7.4 Singular Value Decompositions, Exercise 2

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Adapted from Understanding Linear Algebra © 2023 David Austin. Licensed under CC BY 4.0. Source: Understanding Linear Algebra. Imported at revision 3e6dced.