The prospective candidates of the GATE 2026 Physics (PH) exam must familiarise themselves with the GATE Physics syllabus. The ...

Let $D$ be a linear partial differential operator between vector bundles on a differentiable manifold $X$ of dimension $n$. Let $\mathcal{D}$ be the sheaf of germs of ...

Compact and weakly compact operators on function spaces are studied. Those operators are characterized by properties of finitely additive set functions whose existence is guaranteed by Riesz ...

Linear operators form the cornerstone of analysis in Banach spaces, offering a framework in which one can rigorously study continuity, spectral properties and stability. Banach space theory, with its ...

Pair of Linear Equations in Two Variables Class 10 Notes: Revision notes for CBSE Class 10 Mathematics Chapter 3 Pair of Linear Equations in Two Variables have been presented in the article along with ...

Some important points to revise from the chapter are: • An equation of the form ax + by + c = 0, where a, b and c are real numbers, such that a and b are not both zero, is called a linear equation in ...