Elementary set theory and solution sets of systems of linear equations. An introduction to proofs and the axiomatic methods through a study of the vector space axioms. Linear analytic geometry. Linear ...

A comprehensive theory of the matrix linear equation AX + XB = C is presented. The equation is viewed as a vector equation LX = C in the vector space of all m × n matrices. As the main result, two ...

If \(A\) is a \(3\times 3\) matrix then we can apply a linear transformation to each rgb vector via matrix multiplication, where \([r,g,b]\) are the original values ...

TODD, J. (1) Determinants and Matrices (2) Theory of Equations (3) Integration (4) Vector Methods: Applied to Differential Geometry, Mechanics and Potential Theory (5) Integration of Ordinary ...

Abstract Let A be an n × n Hermitian matrix and A = UΛUH be its spectral decomposition, where U is a unitary matrix of order n and Λ is a diagonal matrix. In this note we present the perturbation ...