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WildLinAlg4: Area and volume

Area and volume in Linear Algebra are central concepts that underpin the entire subject, and lead naturally to the rich theory of determinants, a key subject of 18th and 19th century mathematics.This is the fourth lecture of a first course on Linear Algebra, given by N J Wildberger. Here we start with a pictorial treatment of area, then move to an algebraic formulation using bi-vectors. These are two-dimensional versions of vectors introduced in the 1840's by Grassmann.The three dimensional case of volume uses tri-vectors.CONTENT SUMMARY: pg 1: @00:08 area and volume; setting up affine geometry? as independent of distance;pg 2: @02:03 area of a parallelogram;pg 3: @06:35 general formula for area of a parallelogram; one of the most important formulas in mathematics;pg 4: @11:53 algebraic approach to measuring area; bi-vector (Herman Grassmann); Grassmann algebra;pg 5: @15:11 Bi-vectors; torque;pg 6: @21:14 linear? momentum; conservation of momentum; momentum and force; Bi-vectors; angular momentum; torquepg 7: @25:52 Bi-vector and electromagnetism; cross_product mentioned;pg 8: @28:42 Bi-vectors in the plane; operations on bi-vectors;pg 9: @30:59 bi-vector Distributive laws:pg 10: @34:04 claim: In the plane, every bi-vector is a multiple of the bi-vector of base vectors; geometric proof; algebraic proof (THANKS to EmptySpaceEnterprise)
Length: 56:03


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