.. _book_fig_chapter7_fig_svd_visual:


Plot a visual representation of an SVD
--------------------------------------
Figure 7.3

Singular value decomposition (SVD) can factorize an N x K matrix into
:math:`U \Sigma V^T`. There are different conventions for computing the SVD
in the literature, and this figure illustrates the convention used in this
text. The matrix of singular values :math:`\Sigma` is always a square matrix
of size [R x R] where R = min(N, K). The shape of the resulting U and V
matrices depends on whether N or K is larger. The columns of the matrix U are
called the left-singular vectors, and the columns of the matrix V are called
the right-singular vectors. The columns are orthonormal bases, and satisfy
:math:`U^T U = V^T V = I`.



.. image:: ../images/chapter7/fig_svd_visual_1.png
    :scale: 100
    :align: center


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