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Necessary and sufficient condition: continuous map on semi-normed vector spaces

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#general-topology #vector-spaces #continuity #normed-spaces
73
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Let $A$ be a $(n \times n)$ complex matrix, and for $C$ a $(1 \times n)$ row vector let $W = \{\sum_{j=0}^{n-1}a_jCA^j:j=0,\dots,n-1\}\;.$

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#linear-algebra #matrices #vector-spaces #cayley-hamilton
56
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proving identities of a vector space

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#linear-algebra #abstract-algebra #vector-spaces #binary-operations
168
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Determine if set is linearly independent in folowing vector space

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#linear-algebra #vector-spaces
381
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Different ways to prove a set is a subspace of $\mathbb R^n$

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#linear-algebra #vector-spaces #proof-writing #systems-of-equations
63
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Proving that a basis exists for a vector Subspace

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#linear-algebra #vector-spaces #vectors
96
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Continuous function satisfying axioms

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#vector-spaces #vectors
497
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Is every vector space a proper subspace of a larger vector space?

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#linear-algebra #vector-spaces
98
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What is solution to this vector problem?

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#linear-algebra #vector-spaces #vectors
91
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How to find third point of triangle with specific area?

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#linear-algebra #geometry #vector-spaces
141
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The polynomials $X^k(X-1)^{n-k}$ form a basis of $\mathbb{R_n}[X]$

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#linear-algebra #polynomials #vector-spaces
226
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Prove $\mathbb{R}^n \cong \mathbb{R}$ as vector spaces over $\mathbb{Q}$

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#abstract-algebra #vector-spaces #modules
816
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Vector space isomorphic to direct sum

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#abstract-algebra #vector-spaces #modules #direct-sum #vector-space-isomorphism
184
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Parametrize solution

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#linear-algebra #vector-spaces
214
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Trying to find the dimension of a vector space...

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#linear-algebra #vector-spaces #linear-transformations #vector-space-isomorphism

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