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1. Vectors (from a geometric perspective)
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Vectors: defined geometrically (coordinate-free), how to add and scale them, basic algebraic properties of vector addition and scalar multiplication... proved geometrically. Coordinates and lengths of vectors.
𝐹𝑢𝑙𝑙 𝐹𝑟𝑜𝑛𝑡𝑎𝑙 𝐶𝑎𝑙𝑐𝑢𝑙𝑢𝑠,
𝑇ℎ𝑒 𝐷𝑎𝑟𝑘 𝐴𝑟𝑡 𝑜𝑓 𝐿𝑖𝑛𝑒𝑎𝑟 𝐴𝑙𝑔𝑒𝑏𝑟𝑎,
𝑃𝑟𝑒𝑐𝑎𝑙𝑐𝑢𝑙𝑢𝑠 𝑀𝑎𝑑𝑒 𝐷𝑖𝑓𝑓𝑖𝑐𝑢𝑙𝑡,
𝐿𝑜𝑏𝑎𝑐ℎ𝑒𝑣𝑠𝑘𝑖 𝐼𝑙𝑙𝑢𝑚𝑖𝑛𝑎𝑡𝑒𝑑.
All my books are available for purchase at Amazon.
0:00 Intro
1:00 Vectors as arrows
3:06 Vector addition
4:19 Commutativity of vector addition
6:27 Non-commutative operations
6:59 Associativity of vector addition
8:33 Non-associative operations (Rock Paper Scissors!)
10:20 Scalar multiplication
12:20 Algebraic properties of scalar multiplication
15:14 Vector subtraction
16:37 Towards coordinates - i-hat and j-hat
18:09 A peek under the hood
21:23 Vectors in 3-dimnesional space
23:08 Shorthand vector notation
24:52 Length of a vector
𝐹𝑢𝑙𝑙 𝐹𝑟𝑜𝑛𝑡𝑎𝑙 𝐶𝑎𝑙𝑐𝑢𝑙𝑢𝑠,
𝑇ℎ𝑒 𝐷𝑎𝑟𝑘 𝐴𝑟𝑡 𝑜𝑓 𝐿𝑖𝑛𝑒𝑎𝑟 𝐴𝑙𝑔𝑒𝑏𝑟𝑎,
𝑃𝑟𝑒𝑐𝑎𝑙𝑐𝑢𝑙𝑢𝑠 𝑀𝑎𝑑𝑒 𝐷𝑖𝑓𝑓𝑖𝑐𝑢𝑙𝑡,
𝐿𝑜𝑏𝑎𝑐ℎ𝑒𝑣𝑠𝑘𝑖 𝐼𝑙𝑙𝑢𝑚𝑖𝑛𝑎𝑡𝑒𝑑.
All my books are available for purchase at Amazon.
0:00 Intro
1:00 Vectors as arrows
3:06 Vector addition
4:19 Commutativity of vector addition
6:27 Non-commutative operations
6:59 Associativity of vector addition
8:33 Non-associative operations (Rock Paper Scissors!)
10:20 Scalar multiplication
12:20 Algebraic properties of scalar multiplication
15:14 Vector subtraction
16:37 Towards coordinates - i-hat and j-hat
18:09 A peek under the hood
21:23 Vectors in 3-dimnesional space
23:08 Shorthand vector notation
24:52 Length of a vector
0:27:37
1. Vectors (from a geometric perspective)
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