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3Blue1Brown Series Essence of linear algebra Episode 8 Nonsquare matrices as transformations between dimensions 2016

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Because people asked, this is a video briefly showing the geometric interpretation of non-square matrices as linear transformations that go between dimensions.

Released: 2016-08-16
Runtime: 60 minutes
Genre: Documentary
Stars:
Director: Grant Sanderson

1. Vectors, what even are they? 2016-08-06

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2. Linear combinations, span, and basis vectors 2016-08-07

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3. Linear transformations and matrices 2016-08-07

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4. Matrix multiplication as composition 2016-08-09

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5. Three-dimensional linear transformations 2016-08-10

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6. The determinant 2016-08-11

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7. Inverse matrices, column space and null space 2016-08-16

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8. Nonsquare matrices as transformations between dimensions 2016-08-16

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9. Dot products and duality 2016-08-24

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10. Cross products 2016-09-01

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11. Cross products in the light of linear transformations 2016-09-03

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12. Cramer's rule, explained geometrically 2019-03-17

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13. Change of basis 2016-09-11

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14. Eigenvectors and eigenvalues 2016-09-15

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15. A quick trick for computing eigenvalues 2021-05-07

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16. Abstract vector spaces 2016-09-24

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