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The geometric mean of two positive definite (Hermitian) matrices of same size is defined by $$A\natural B := A^{1/2}(A^{-1/2}BA^{-1/2})^{1/2}A^{1/2},$$equivalently, $$A\natural B =(BA^{-1})^{1/2}A=A(A^...

I want to construct an $n$-simplex the following way: Choose $n$ vectors in the boundary of an $n$ dimensional ball, which are forming an $(n-1)$-simplex together. Place the orthogonal affine $n-1$-...

Goal I'm interested in describing Möbius transformations in the plane, and I'd like to define them in terms of three points and their images. What I have tried I know that a projective ...

The complex inner product $\langle u, v \rangle$ is a special case of a sesquilinear form over a field. Its definition is $\langle u, v \rangle = \sum_{i} u_i \overline{v_i}$. There is clearly the ...