Linear transformations and matrices

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1. Linear combinations, span, and basis vectors

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2. The determinant

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3. Matrix multiplication as composition

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4. Nonsquare matrices as transformations between dimensions

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5. Vectors, what even are they?

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6. Inverse matrices, column space and null space

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7. Eigenvectors and eigenvalues

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8. Dot products and duality

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9. Integration and the fundamental theorem of calculus

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10. Derivative formulas through geometry

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11. Implicit differentiation, what's going on here?

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12. A quick trick for computing eigenvalues

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