Geodesic
The case of equality in the generalized Wielandt inequality
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIV, Tome 268 (2000), pp. 86-94 
L. Yu. Kolotilina. The case of equality in the generalized Wielandt inequality. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIV, Tome 268 (2000), pp. 86-94. http://geodesic.mathdoc.fr/item/ZNSL_2000_268_a5/
@article{ZNSL_2000_268_a5,
     author = {L. Yu. Kolotilina},
     title = {The case of equality in the generalized {Wielandt} inequality},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {86--94},
     year = {2000},
     volume = {268},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_268_a5/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

This note provides a description of all those pairs of nonzero vectors $x,y\in\mathbb C_n$, $n\ge2$, for which the generalized Wielandt inequality $$ |x^*Ay|^2\le\Biggr[\frac{\lambda_1-\lambda_n+(\lambda_1+\lambda_n)|\varphi|}{\lambda_1+\lambda_n+(\lambda_1-\lambda_n)|\varphi|}\Biggl]^2x^*Ax\,\,y^*Ay, \ \varphi=\frac{x^*y}{\|x\|\,\|y\|}, $$ where $A\in\mathbb C^{n\times n}$ is an Hermitian positive-definite matrix with eigenvalues $\lambda_1\ge\lambda_2\ge\cdots\ge\lambda_n$ such that $\lambda_1>\lambda_n$, holds with equality.