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Vector spanning a space

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#linear-algebra #vector-spaces
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Orthogonal projection of a point to plane

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#linear-algebra #vector-spaces
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Cosine similarity vs angular distance

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#vector-spaces #vectors
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Show that given vectors are not vector space basis in $R^4$

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#vector-spaces
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Can the given vector be expressed as a linear combination of the other three

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#vector-spaces
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Let $W_{1},W_{2}$ be sub-spaces of $\mathbb{R}^{4}$, find a subspace $W_{3}$ s.t $W_3\subset W_{2}$ and $W_{1}\oplus W_{3}=W_{1}+W_{2}$

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#linear-algebra #vector-spaces
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Simplex in a complex vector space

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#vector-spaces #convex-analysis #simplex
344
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Show that four points given by vectors lay on a circle

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#geometry #vector-spaces #vectors #vector-analysis #circles
54
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$\text{proj} _{u_1}v + \text{proj} _{u_2}v = \text{proj} _{U}v$

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#linear-algebra #vector-spaces
136
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Can the "symmetric algebra" over $\mathbb R^n$ be defined from an infinite-dimensional exterior algebra?

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#abstract-algebra #vector-spaces #infinity #exterior-algebra #symmetric-polynomials
203
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Annihilator in dual space

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#linear-algebra #vector-spaces #linear-transformations #constructive-mathematics #dual-spaces
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show that $\operatorname{rank}(g\circ f) \leq \operatorname{rank}(f)+\operatorname{rank}(g)-n$

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#linear-algebra #vector-spaces #linear-transformations
130
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Element which is independent

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#linear-algebra #vector-spaces #change-of-basis
140
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Determining eigenvalues of a linear transformation on a field extension via embedding into $\Bbb{C}$

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#vector-spaces #field-theory #linear-transformations
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How to construct a matrix given the null basis of A?

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#linear-algebra #matrices #vector-spaces

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