3 citations · 7 across the 6 of their papers we have counts for
6 papers
Parity of n-Frames with Application to Non-Procrustean Orthogonalization
Jon A. Sjogren
The space of complete orthonormal frames in Euclidean space is not path connected. In fact it has exactly two path components, containing respectively the coordinate frame of n sta…
Complex Axis and de Medeiros' Campo Vetorial
Jon A. Sjogren
The Complex Axis theorem states that any endomorphism of a finite-dimensional complex vector space affords an eigen-vector (or "invariant axis"). A geometric proof of this geometri…
Homogeneous Systems and Euclidean Topology
Jon A. Sjogren
The Theorem on Invariance of Domain due to L.E.J. Brouwer states that one connected, compact (Hausdorff) m-dimensional manifold embedded into another actually realizes a homeomorph…
Complex Odd-Dimensional Endomorphism and Topological Degree
Jon A. Sjogren
A linear mapping upon real n-dimensional space, where the dimension n is odd, has a real eigenvalue-eigenvector pair. The corresponding statement for complex vector spaces holds tr…
Polynomial Roots and Open Mappings
Jon A. Sjogren
The "openness" of a complex polynomial mapping is discussed and applied to the Fundamental Theorem of Algebra. In this category fall proofs of S. Wolfenstein, R.L. Thompson, J. Mil…
Real Polynomial Rings and Domain Invariance
Jon A. Sjogren
Recent proofs of classical theorems in polynomial algebra and functional analysis are discussed, which use tools from the topology of real manifolds. Simpler proofs were discovered…