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When do symmetries enforce gaplessness? In 1+1 dimensions, we give a span criterion that certifies gaplessness from partial ...

Definition and problems based on checking linear combination or not.

... the other is whether the vectors could be generated i mean whether the vectors span the B span the vector space but if we know ...

... just your unit vectors those obviously span R3 it's a standard basis and that's an example of an orthogonal list of vectors and so I ...

This project was created with Explain Everything™ Interactive Whiteboard for iPad. 00:00 Slide 1 00:13 Slide 2 02:05 Slide 3 ...

Chapter 3: Normed and Inner Product Spaces, ONBs, Projections, part 3.

In this video, I explain the Basis of a Vector Space in a simple and clear way, with easy examples. This video will help you ...

In this video, I introduce the concept of linear maps and their properties such as additivity and homogeneity, going on to talk about ...

scshape Let $X$ be a normed vector space over $\mathbb{R}$. Show that $X$ is separable if and only if there exists a separable ...

The following subspace the s nal here the s orthogonal is all the vectors of the form from zero something zero which is the span of ...

Chapter 3: Normed and Inner Product Spaces, ONBs, Projections, part 2.

Chapter 7: Topology sigma(E,F), weak and weak-* topologies, part 1.

Tangent space, Tangent bundle, Algebraic definition of tangent space, Germs of smooth functions, Derivations, Geometric ...

Chapter 5: Linear Functionals and the Hahn-Banach Theorem, part 3. Chapter 6: Dual and bidual spaces, part 1.

In this video, I introduce two important subspaces related to linear maps, namely the kernel and image. At the end of the video, I tie ...

In this video, we explore one of the most important mathematical foundations of quantum mechanics — the Fundamental Theorem ...