svd

Singular Value Decomposition.

📝Syntax

s = svd(M)
[U, S, V] = svd(M)
[U, S, V] = svd(M, 0)
[U, S, V] = svd(M, 'econ')

📥Input Arguments

Parameter	Description
M	a numeric value: matrix (double or single)

📤Output Arguments

Parameter	Description
s	real vector (singular values) by descending order.
U	left singular values.
S	real diagonal matrix (singular values)
V	right singular values.

📄Description

svd computes the Singular Value Decomposition of a matrix.

For an

$$m \times n$$

matrix M, the SVD is:

$$M = U\Sigma V^T$$

where:

$$m \times m$$

unitary matrix (left singular vectors)

$$m \times n$$

diagonal matrix with non-negative real numbers (singular values)

$$n \times n$$

unitary matrix (right singular vectors)

The singular values

$$\sigma_i$$

are arranged in decreasing order:

$$\sigma_1 \geq \sigma_2 \geq \ldots \geq 0$$

💡Examples

X = eye(3, 3);
s = svd(X)
[U, S, V] = svd(X)

🔗See Also

🕔Version History

Version	Description
1.0.0	initial version