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The Bright Side of Mathematics
Linear Algebra [dark version]
31,719 views
66 items
Last updated on Dec 19, 2023
public playlist
See tbsom.de/s/la
The Bright Side of Mathematics
4:28
Linear Algebra 1 | Introduction [dark version]
The Bright Side of Mathematics
7:23
Linear Algebra 2 | Vectors in ℝ² [dark version]
The Bright Side of Mathematics
11:24
Linear Algebra 3 | Linear Combinations and Inner Products in ℝ² [dark version]
The Bright Side of Mathematics
7:53
Linear Algebra 4 | Lines in ℝ² [dark version]
The Bright Side of Mathematics
10:20
Linear Algebra 5 | Vector Space ℝn [dark version]
The Bright Side of Mathematics
9:36
Linear Algebra 6 | Linear Subspaces [dark version]
The Bright Side of Mathematics
10:58
Linear Algebra 7 | Examples for Subspaces [dark version]
The Bright Side of Mathematics
8:02
Linear Algebra 8 | Linear Span [dark version]
The Bright Side of Mathematics
12:26
Linear Algebra 9 | Inner Product and Norm [dark version]
The Bright Side of Mathematics
13:15
Linear Algebra 10 | Cross Product [dark version]
The Bright Side of Mathematics
10:16
Linear Algebra 11 | Matrices [dark version]
The Bright Side of Mathematics
12:55
Linear Algebra 12 | Systems of Linear Equations [dark version]
The Bright Side of Mathematics
7:39
Linear Algebra 13 | Special Matrices [dark version]
The Bright Side of Mathematics
5:24
Linear Algebra 14 | Column Picture of the Matrix-Vector Product [dark version]
The Bright Side of Mathematics
7:59
Linear Algebra 15 | Row Picture [dark version]
The Bright Side of Mathematics
8:37
Linear Algebra 16 | Matrix Product [dark version]
The Bright Side of Mathematics
10:53
Linear Algebra 17 | Properties of the Matrix Product [dark version]
The Bright Side of Mathematics
7:50
Linear Algebra 18 | Linear Maps (Definition) [dark version]
The Bright Side of Mathematics
10:32
Linear Algebra 19 | Matrices induce linear maps [dark version]
The Bright Side of Mathematics
8:47
Linear Algebra 20 | Linear maps induce matrices [dark version]
The Bright Side of Mathematics
6:47
Linear Algebra 21 | Examples of Linear Maps [dark version]
The Bright Side of Mathematics
6:30
Linear Algebra 22 | Linear Independence (Definition) [dark version]
The Bright Side of Mathematics
6:53
Linear Algebra 23 | Linear Independence (Examples) [dark version]
The Bright Side of Mathematics
7:25
Linear Algebra 24 | Basis of a subspace [dark version]
The Bright Side of Mathematics
8:39
Linear Algebra 25 | Coordinates with respect to a Basis [dark version]
The Bright Side of Mathematics
9:58
Linear Algebra 26 | Steinitz Exchange Lemma [dark version]
The Bright Side of Mathematics
7:12
Linear Algebra 27 | Dimension of a Subspace [dark version]
The Bright Side of Mathematics
13:14
Linear Algebra 28 | Conservation of Dimension [dark version]
The Bright Side of Mathematics
11:03
Linear Algebra 29 | Identity and Inverses [dark version]
The Bright Side of Mathematics
10:19
Linear Algebra 30 | Injectivity, Surjectivity for Square Matrices [dark version]
The Bright Side of Mathematics
7:04
Linear Algebra 31 | Inverses of Linear Maps are Linear [dark version]
The Bright Side of Mathematics
7:28
Linear Algebra 32 | Transposition for Matrices [dark version]
The Bright Side of Mathematics
7:57
Linear Algebra 33 | Transpose and Inner Product [dark version]
The Bright Side of Mathematics
8:58
Linear Algebra 34 | Range and Kernel of a Matrix [dark version]
The Bright Side of Mathematics
14:34
Linear Algebra 35 | Rank-Nullity Theorem [dark version]
The Bright Side of Mathematics
9:28
Linear Algebra 36 | Solving Systems of Linear Equations (Introduction) [dark version]
The Bright Side of Mathematics
15:52
Linear Algebra 37 | Row Operations [dark version]
The Bright Side of Mathematics
11:17
Linear Algebra 38 | Set of Solutions [dark version]
The Bright Side of Mathematics
13:17
Linear Algebra 39 | Gaussian Elimination [dark version]
The Bright Side of Mathematics
16:04
Linear Algebra 40 | Row Echelon Form [dark version]
The Bright Side of Mathematics
11:34
Linear Algebra 41 | Solvability of a System [dark version]
The Bright Side of Mathematics
6:53
Linear Algebra 42 | Uniqueness of Solutions [dark version]
The Bright Side of Mathematics
7:07
Linear Algebra 43 | Determinant (Overview) [dark version]
The Bright Side of Mathematics
12:34
Linear Algebra 44 | Determinant in 2 Dimensions [dark version]
The Bright Side of Mathematics
14:07
Linear Algebra 45 | Determinant is a Volume Measure [dark version]
The Bright Side of Mathematics
9:54
Linear Algebra 46 | Leibniz Formula for Determinants [dark version]
The Bright Side of Mathematics
10:27
Linear Algebra 47 | Rule of Sarrus [dark version]
The Bright Side of Mathematics
9:59
Linear Algebra 49 | Formulas for Determinants [dark version]
The Bright Side of Mathematics
11:24
Linear Algebra 50 | Gaussian Elimination for Determinants [dark version]
The Bright Side of Mathematics
12:18
Linear Algebra 48 | Laplace Expansion [dark version]
The Bright Side of Mathematics
12:45
Linear Algebra 52 | Cramer's Rule [dark version]
The Bright Side of Mathematics
10:04
Linear Algebra 51 | Determinant for Linear Maps [dark version]
The Bright Side of Mathematics
12:42
Linear Algebra 53 | Eigenvalues and Eigenvectors [dark version]
The Bright Side of Mathematics
12:22
Linear Algebra 54 | Characteristic Polynomial [dark version]
The Bright Side of Mathematics
11:44
Linear Algebra 55 | Algebraic Multiplicity [dark version]
The Bright Side of Mathematics
9:38
Linear Algebra 56 | Geometric Multiplicity [dark version]
The Bright Side of Mathematics
8:24
Linear Algebra 57 | Spectrum of Triangular Matrices [dark version]
The Bright Side of Mathematics
11:52
Linear Algebra 58 | Complex Vectors and Complex Matrices [dark version]
The Bright Side of Mathematics
11:15
Linear Algebra 59 | Adjoint [dark version]
The Bright Side of Mathematics
15:17
Linear Algebra 60 | Selfadjoint and Unitary Matrices [dark version]
The Bright Side of Mathematics
8:41
Linear Algebra 61 | Similar Matrices [dark version]
The Bright Side of Mathematics
14:41
Linear Algebra 62 | Recipe for Calculating Eigenvectors [dark version]
The Bright Side of Mathematics
13:25
Linear Algebra 63 | Spectral Mapping Theorem [dark version]
The Bright Side of Mathematics
11:06
Linear Algebra 64 | Diagonalization [dark version]
The Bright Side of Mathematics
13:45
Linear Algebra 65 | Diagonalizable Matrices [dark version]
The Bright Side of Mathematics
14:28
QR decomposition (for square matrices) [dark version]
![Linear Algebra 1 | Introduction [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/SrhtsGd0y1s/sddefault.jpg&local=true)
![Linear Algebra 2 | Vectors in ℝ² [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/edqg1mnjsog/sddefault.jpg&local=true)
![Linear Algebra 3 | Linear Combinations and Inner Products in ℝ² [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/kOhynwtKXSo/sddefault.jpg&local=true)
![Linear Algebra 4 | Lines in ℝ² [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/N9rtX7KlHwg/sddefault.jpg&local=true)
![Linear Algebra 5 | Vector Space ℝn [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/iLqz7UTC7uw/sddefault.jpg&local=true)
![Linear Algebra 6 | Linear Subspaces [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/-haS6TdpcSU/sddefault.jpg&local=true)
![Linear Algebra 7 | Examples for Subspaces [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/0c2nHH03JdE/sddefault.jpg&local=true)
![Linear Algebra 8 | Linear Span [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/okGwr0vpufQ/sddefault.jpg&local=true)
![Linear Algebra 9 | Inner Product and Norm [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/fXWdBineqWI/sddefault.jpg&local=true)
![Linear Algebra 10 | Cross Product [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/sa8REnW-p8o/sddefault.jpg&local=true)
![Linear Algebra 11 | Matrices [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/_sS8-H9uUdU/sddefault.jpg&local=true)
![Linear Algebra 12 | Systems of Linear Equations [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/5Qeh5crG1bI/sddefault.jpg&local=true)
![Linear Algebra 13 | Special Matrices [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/GJrb55b6FCU/sddefault.jpg&local=true)
![Linear Algebra 14 | Column Picture of the Matrix-Vector Product [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/P56YTeY2YzM/sddefault.jpg&local=true)
![Linear Algebra 15 | Row Picture [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/8BPVI2CPSF0/sddefault.jpg&local=true)
![Linear Algebra 16 | Matrix Product [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/RQxqdlqhH-Y/sddefault.jpg&local=true)
![Linear Algebra 17 | Properties of the Matrix Product [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/Q6G3amKjhtQ/sddefault.jpg&local=true)
![Linear Algebra 18 | Linear Maps (Definition) [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/lJnwwbwPE-8/sddefault.jpg&local=true)
![Linear Algebra 19 | Matrices induce linear maps [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/0e47221ZMuA/sddefault.jpg&local=true)
![Linear Algebra 20 | Linear maps induce matrices [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/jZqb1RwbCCw/sddefault.jpg&local=true)
![Linear Algebra 21 | Examples of Linear Maps [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/vG54BGp9Ikg/sddefault.jpg&local=true)
![Linear Algebra 22 | Linear Independence (Definition) [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/q66L7aw1QyE/sddefault.jpg&local=true)
![Linear Algebra 23 | Linear Independence (Examples) [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/062Iy-pbGug/sddefault.jpg&local=true)
![Linear Algebra 24 | Basis of a subspace [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/6VZiuEyTQVY/sddefault.jpg&local=true)
![Linear Algebra 25 | Coordinates with respect to a Basis [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/NDDFJRinngk/sddefault.jpg&local=true)
![Linear Algebra 26 | Steinitz Exchange Lemma [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/OjWEEFASnVo/sddefault.jpg&local=true)
![Linear Algebra 27 | Dimension of a Subspace [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/Pqi87Stwomw/sddefault.jpg&local=true)
![Linear Algebra 28 | Conservation of Dimension [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/Ba4ycLfI5Rc/sddefault.jpg&local=true)
![Linear Algebra 29 | Identity and Inverses [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/YvlnqA2gXQk/sddefault.jpg&local=true)
![Linear Algebra 30 | Injectivity, Surjectivity for Square Matrices [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/MxTh_FMkKHE/sddefault.jpg&local=true)
![Linear Algebra 31 | Inverses of Linear Maps are Linear [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/zcf0kmUJMU4/sddefault.jpg&local=true)
![Linear Algebra 32 | Transposition for Matrices [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/1Kgzsnq0hUo/sddefault.jpg&local=true)
![Linear Algebra 33 | Transpose and Inner Product [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/sVCRIH3a1ro/sddefault.jpg&local=true)
![Linear Algebra 34 | Range and Kernel of a Matrix [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/4mv_wxw4u6s/sddefault.jpg&local=true)
![Linear Algebra 35 | Rank-Nullity Theorem [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/jPyxiNY7a88/sddefault.jpg&local=true)
![Linear Algebra 36 | Solving Systems of Linear Equations (Introduction) [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/bOirYo1OjD8/sddefault.jpg&local=true)
![Linear Algebra 37 | Row Operations [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/VupBUH8WeIw/sddefault.jpg&local=true)
![Linear Algebra 38 | Set of Solutions [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/orIOFtmgG0c/sddefault.jpg&local=true)
![Linear Algebra 39 | Gaussian Elimination [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/mCm5ZstHFcc/sddefault.jpg&local=true)
![Linear Algebra 40 | Row Echelon Form [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/kCp7cTwli0M/sddefault.jpg&local=true)
![Linear Algebra 41 | Solvability of a System [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/_PGP0Zm8iAQ/sddefault.jpg&local=true)
![Linear Algebra 42 | Uniqueness of Solutions [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/n5miMS-PwpM/sddefault.jpg&local=true)
![Linear Algebra 43 | Determinant (Overview) [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/UYuJvRyDzN0/sddefault.jpg&local=true)
![Linear Algebra 44 | Determinant in 2 Dimensions [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/XmFSotdmpKc/sddefault.jpg&local=true)
![Linear Algebra 45 | Determinant is a Volume Measure [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/liDIaNGeaMM/sddefault.jpg&local=true)
![Linear Algebra 46 | Leibniz Formula for Determinants [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/2ddRZsBdzJc/sddefault.jpg&local=true)
![Linear Algebra 47 | Rule of Sarrus [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/aYCy__Yghyo/sddefault.jpg&local=true)
![Linear Algebra 49 | Formulas for Determinants [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/MXIe76m-UZA/sddefault.jpg&local=true)
![Linear Algebra 50 | Gaussian Elimination for Determinants [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/qMU1wHa8ZTw/sddefault.jpg&local=true)
![Linear Algebra 48 | Laplace Expansion [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/8LOE_mKJooM/sddefault.jpg&local=true)
![Linear Algebra 52 | Cramer's Rule [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/BXcueJ7EyM4/sddefault.jpg&local=true)
![Linear Algebra 51 | Determinant for Linear Maps [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/lPwRryR-ILc/sddefault.jpg&local=true)
![Linear Algebra 53 | Eigenvalues and Eigenvectors [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/D02YcCTFO0Q/sddefault.jpg&local=true)
![Linear Algebra 54 | Characteristic Polynomial [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/CgmJeDZSLMY/sddefault.jpg&local=true)
![Linear Algebra 55 | Algebraic Multiplicity [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/kVFlpNUqC40/sddefault.jpg&local=true)
![Linear Algebra 56 | Geometric Multiplicity [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/qcuDtwu_zL4/sddefault.jpg&local=true)
![Linear Algebra 57 | Spectrum of Triangular Matrices [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/NORBi0mxhLU/sddefault.jpg&local=true)
![Linear Algebra 58 | Complex Vectors and Complex Matrices [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/xf4O4P2sJjo/sddefault.jpg&local=true)
![Linear Algebra 59 | Adjoint [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/ozUjXKQnJCU/sddefault.jpg&local=true)
![Linear Algebra 60 | Selfadjoint and Unitary Matrices [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/EQAwDusylE4/sddefault.jpg&local=true)
![Linear Algebra 61 | Similar Matrices [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/k_K8sbOuuBc/sddefault.jpg&local=true)
![Linear Algebra 62 | Recipe for Calculating Eigenvectors [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/F1YjR5cglIQ/sddefault.jpg&local=true)
![Linear Algebra 63 | Spectral Mapping Theorem [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/r9ZWx1NKNX0/sddefault.jpg&local=true)
![Linear Algebra 64 | Diagonalization [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/xrdUXznKZXQ/sddefault.jpg&local=true)
![Linear Algebra 65 | Diagonalizable Matrices [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/PSbPuQDPg-I/sddefault.jpg&local=true)
![QR decomposition (for square matrices) [dark version]](/api/proxy/image?url=https://i.ytimg.com/vi/y80VF1iJGCY/sddefault.jpg&local=true)