TITLE: Geometric interpretation of normal and anti-hermitian matrices
QUESTION [12 upvotes]: How do I interpret following types of matrices as special types of transformations?
I mean what are the transformative properties of following types of matrices, from $\mathbb{R}^n $ to $ \mathbb{R}^n$, or $\mathbb{C^n}$ to $\mathbb{C^n}$?
Normal and Anti Hermitian Matrices?
ADDED
I expect answer something like this for orthogonal matrices Quoting Wikipedia: 
As a linear transformation, an orthogonal matrix preserves the dot product of vectors, and therefore acts as an isometry of Euclidean space, such as a rotation or reflection. In other words, it is a unitary transformation.
ADDED
I managed to collect some more information:
Unitary matrices as Linear Maps preserve inner products, may be not necessarily for reals only, as orthogonal ones(???).

REPLY [3 votes]: Wikipedia lists about 10 properties of a linear transformation that are equivalent with normality. Here is a property with a geometrical touch that is not mentioned there (it's an exercice in Halmos' Finite-dimensional vector spaces):
A linear transformation $A:\ V\to V$ of a finite-dimensional unitary space is normal iff the orthogonal complement of any invariant subspace is  invariant as well.