Euclidean spaces
- Page ID
- 22648
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- Basis and dimension
- 4.2.11.pg
- 4.2.12.pg
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- 4.2.15.pg
- 4.2.17 21a.pg
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- Basis 01a.pg
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- Basis 02a.pg
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- Basis 03a.pg
- Basis 03b.pg
- Basis 04a.pg
- Basis 04b.pg
- Basis 05a.pg
- Basis 05b.pg
- expandBasis.pg
- Graphical 02.pg
- problem5.pg
- problem6.pg
- problem7.pg
- problem8.pg
- problem9.pg
- Span ind 01.pg
- Span ind 02.pg
- Span ind 03.pg
- Span ind 04.pg
- ur la 10 1.pg
- ur la 10 23.pg
- ur la 10 24.pg
- ur la 10 25.pg
- ur la 10 26.pg
- ur la 10 32.pg
- ur la 9 11.pg
- ur la 9 12.pg
- ur la 9 13.pg
- Linear combinations
- 2.1.15.pg
- 2.1.17.pg
- 2.1.19.pg
- 2.1.27.pg
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- 2.1.4.pg
- 2.1.49.pg
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- 2.1.52.pg
- 2.1.53.pg
- 2.1.6.pg
- 2.1.64.pg
- guessCoefficients.pg
- Lin combi 01a.pg
- Lin combi 01b.pg
- Lin combi 02a.pg
- Lin combi 02b.pg
- Lin combi 03a.pg
- Lin combi 03b.pg
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- problem2.pg
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- problem5.pg
- ur la 8 10.pg
- ur la 8 8.pg
- ur la 9 10.pg
- Linear independence
- 2.3.10.pg
- 2.3.11.pg
- 2.3.13.pg
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- Dep 01a.pg
- Dep 01b.pg
- Dep 02a.pg
- Dep 02b.pg
- Dep 04.pg
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- Graphical 01.pg
- Ind 01a.pg
- Ind 01b.pg
- Ind 03.pg
- problem10.pg
- problem11.pg
- problem3.pg
- problem4.pg
- problem5.pg
- problem8.pg
- prob 1.pg
- prob 4.pg
- prob 5.pg
- ur la 9 1a.pg
- ur la 9 3.pg
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- ur la 9 7.pg
- ur la 9 9.pg
- Row, column, and null spaces
- 4.1.22.pg
- 4.1.23.pg
- 4.1.27.pg
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- 4.1.46.pg
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- 4.3.43 52a.pg
- 4.3.46.pg
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- 4.3.5.pg
- 4.3.6.pg
- Basis 10.pg
- Basis 10 null space.pg
- Basis 11.pg
- Basis 11 column space.pg
- Basis 12.pg
- Basis 12 row space.pg
- Basis 13.pg
- Basis 13 null space.pg
- Basis 14.pg
- Basis 14 column space.pg
- Basis 15.pg
- Basis 15 null space.pg
- Basis 16.pg
- Basis 16 row space.pg
- Basis 17.pg
- Basis 17 row space.pg
- Basis 18.pg
- Basis 18 column space.pg
- Basis 19.pg
- Basis 19 column space.pg
- Basis 30.pg
- Basis 31.pg
- problem1.pg
- problem10.pg
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- problem6.pg
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- ur la 10 11a.pg
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- ur la 10 28.pg
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- Span
- 2.2.10.pg
- 2.2.11.pg
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- 2.2.77.pg
- 2.2.8.pg
- 2.3.26.pg
- 2.3.28.pg
- 2.3.30.pg
- 2.3.72.pg
- guessDependent.pg
- problem1.pg
- problem10.pg
- problem13.pg
- problem2.pg
- problem3.pg
- problem4.pg
- problem5.pg
- problem6.pg
- problem7.pg
- problem8.pg
- problem9.pg
- ur la 9 8.pg
- Subspaces
- 4.1.11.pg
- 4.1.12.pg
- 4.1.16.pg
- 4.1.3.pg
- 4.1.45.pg
- 4.1.50 58a.pg
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- 4.1.53.pg
- 4.1.58.pg
- 4.1.6.pg
- 4.1.7.pg
- 4.1.73.pg
- 4.1.75.pg
- 4.1.9.pg
- problem3.pg
- problem4.pg
- problem5.pg
- Subspaces nonempty 01.pg
- Subspaces nonempty 02.pg
- Subspaces nonempty 03.pg
- Subspaces nonempty 04.pg
- Subspaces nonempty 05.pg
- Subspaces nonempty 06.pg
- Subspaces nonempty 07.pg
- Subspaces nonempty 08.pg
- Subspaces zero 01.pg
- Subspaces zero 02.pg
- Subspaces zero 03.pg
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- Subspaces zero 06.pg
- Subspaces zero 07.pg
- Subspaces zero 08.pg
- ur la 8 6.pg

