奇异值分解

Singular Value Decomposition

In the singular value decomposition $A = U\Sigma V^\top$, the matrices $U$ and $V$ satisfy

Singular Value Decomposition (2)

Singular Value Decomposition (3)

Singular Value Decomposition (4)

Singular Value Decomposition (5)

Singular Value Decomposition (6)

Singular Value Decomposition (7)

Singular Value Decomposition (8)

The singular values of $A$ are the square roots of

An $m \times n$ matrix has at most ______ nonzero singular values.