Let $\mathbb F\in\{\mathbb R,\mathbb C\}$, and let $m,n\in\mathbb N$. Let $A\in\mathbb F^{m\times n}$ be regarded as a [linear map](/page/Linear%20Map) $A:\mathbb F^n\to\mathbb F^m$, where both spaces are equipped with the Euclidean norm. Then
Here $A^*$ denotes the transpose of $A$ when $\mathbb F=\mathbb R$ and the conjugate transpose of $A$ when $\mathbb F=\mathbb C$, and $\lambda_{\max}(A^*A)$ denotes the largest eigenvalue of the Hermitian positive semidefinite matrix $A^*A$.