# geomean

geomean is a convexity aware operator for geometric mean

### Syntax

```
y = geomean(x)
```

### Comments

The operator behaves like the built-in **geomean** command, with the addition that geomean applied to an Hermitian matrix returns the geometric mean of the eigenvalues.

The operator is implemented using a graph representation based on SOCP (standard vector case) and SDP (for the eigenvalue case) reformulations, and can thus only be used in scenarios where YALMIP can propagate convexity and use conic epigraph representations.

The geometric mean of the eigenvalues of a symmetric positive semidefinite matrix is a monotonic function of the determinant, and can thus be used as an alternative in determinant maximization

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