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Is Hamel Basis necessarily uncountable?

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#linear-algebra #hamel-basis
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Applications of real numbers being a vector space over the rational numbers

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#real-analysis #linear-algebra #vector-spaces #applications #hamel-basis
151
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About Cauchy's Functional Equation

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#real-analysis #analysis #hamel-basis
65
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Give a basis for $S = \{M \in \mathcal{M}_3(\mathbb{K})\ |\ \text{Tr}(M) = 0 \wedge \sum_{j=1}^3 M_{i,j} = 0\}$

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#linear-algebra #matrices #vector-spaces #hamel-basis
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linear combination, span, independence and bases for infinite dimensional vector spaces.

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#linear-algebra #vector-spaces #hamel-basis
29
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Polynomial Sub-Spaces

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#linear-algebra #polynomials #vector-spaces #hamel-basis
37
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Let's say there are 2 basis spanning a subspace. One of the basis is a scalar multiple of the other basis?

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#linear-algebra #vector-spaces #hamel-basis
141
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On linear combinations and bases in $\ell^\infty$

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#functional-analysis #vector-spaces #banach-spaces #hamel-basis
61
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Showing that this vector space is infinite dimensional

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#sequences-and-series #functional-analysis #vector-spaces #hamel-basis
580
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Two basis for a vector Space $V$ has the same coordinates. Does that follow both basis are identical?

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#linear-algebra #vector-spaces #hamel-basis
131
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Define continuous functions mapping real numbers between [0, 1] to basis elements of C^n

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#linear-algebra #complex-numbers #hamel-basis
56
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Are those 2 questions asking about the same thing?

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#functional-analysis #normed-spaces #hamel-basis
118
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What's the dimension of $K^S$ for arbitrary $S$?

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#linear-algebra #functional-analysis #cardinals #hamel-basis
209
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Uncountable Hamel basis of Banach space

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#functional-analysis #normed-spaces #hamel-basis
218
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Baire Category Theorem in infinite- dimensional space

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#functional-analysis #hamel-basis

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