MathAlgebraLinear algebraMatrix decomposition

Singular value decomposition

SVD of a 2x2 matrix

Report a typo

Consider a matrix: $A=\begin{pmatrix} -1 & 3 \\ 3 & -1 \\ \end{pmatrix}$ Compute a SVD for $A$ .

Select one option from the list

U=\frac{1}{\sqrt{2}} \begin{pmatrix} 1 & 1 \\ -1 & 1 \\ \end{pmatrix} \qquad \Sigma= \begin{pmatrix} -2 & 0 \\ 0 & -2 \end{pmatrix} \qquad V=\frac{1}{\sqrt{2}} \begin{pmatrix} -1 & 1 \\ 1 & 1 \\ \end{pmatrix}

U=\frac{1}{\sqrt{3}} \begin{pmatrix} 1 & 1 \\ 1 & -1 \\ \end{pmatrix} \qquad \Sigma= \begin{pmatrix} 4 & 0 \\ 0 & 2 \end{pmatrix} \qquad V=\frac{1}{\sqrt{3}} \begin{pmatrix} -1 & 1 \\ 1 & 1 \\ \end{pmatrix}

U=\frac{1}{\sqrt{2}} \begin{pmatrix} 1 & 1 \\ 1 & 1 \\ \end{pmatrix} \qquad \Sigma= \begin{pmatrix} 3 & 2 \\ 3 & 2 \end{pmatrix} \qquad V=\frac{1}{\sqrt{2}} \begin{pmatrix} 1 & -1 \\ 1 & 1 \\ \end{pmatrix}

U=\frac{1}{\sqrt{2}} \begin{pmatrix} 1 & 1 \\ -1 & 1 \\ \end{pmatrix} \qquad \Sigma= \begin{pmatrix} 4 & 0 \\ 0 & 2 \end{pmatrix} \qquad V=\frac{1}{\sqrt{2}} \begin{pmatrix} -1 & 1 \\ 1 & 1 \\ \end{pmatrix}

___

Create a free account to access the full topic