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 argument

• M - a numeric value: matrix (double or single)

📤 Output argument

• 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:

• $U$ is an $m \times m$

unitary matrix (left singular vectors)

• $\Sigma$ is an $m \times n$

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

• $V^T$ is an $n \times n$

unitary matrix (right singular vectors)

The singular values $\sigma_i$

are arranged in decreasing order: $\sigma_1 \geq \sigma_2 \geq \ldots \geq 0$

💡 Example

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

🔗 See also

eig.

🕔 History

Version	📄 Description
1.0.0	initial version