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We define a subset of the closure of the upper half plane associated with anendomorphism on a real inner product space, which is called the leaf. When thedimension of the space is at least 3, the leaf is a convex with respect to thePoincar\'e metric, and contains all eigenvalues with nonnegative imaginarypart. Moreover, the leaf of a normal endomorphism is the minimum Poincar\'econvex domain containing all eigenvalues with nonnegative imaginary part. Themost commonly studied convex domain containing eigenvalues is number range.Numerical range is convex with respect to the Euclidean metric on $\mathbb C$,so numerical range has less information than leaf about real eigenvalues. Weprovide a new visual approach to endomorphisms.

Leaf as a Poincar\'e convex domain associated with an endomorphism on a real inner product space