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Vectors
A vector is a list of numbers, and also an arrow.
Transcript
A vector is a list of numbers. Like this one: three, two.
Order matters. Two, three is a different vector.
A list of two numbers can also be drawn as an arrow. Start in the middle of a flat grid.
The first number says how far to go right: three.
The second says how far to go up: two.
Draw an arrow from the start to where you land. That arrow is the vector.
Negative numbers go left, or down. Minus two, one points up and to the left.
Every list of two numbers is an arrow, and every arrow is a list of two numbers.
With three numbers, the arrow points into space.
With hundreds of numbers, we can't draw it anymore. But it is still just a list.
Needs
Nothing in the tree. This is a starting point; it assumes only arithmetic, basic algebra, functions and their graphs, exponents, square roots.
Leads to
- Adding and scaling vectors video
Add vectors entry by entry (tip to tail); scale by multiplying every entry. - Dot product video
Multiply matching entries and add them up; one number that measures agreement. - Matrices video
A matrix is a grid of numbers; a stack of vectors. - Exp and softmax video
Turn any vector of scores into positive weights that add up to one. - Nonlinearity (ReLU) video
Clip negatives to zero, entry by entry; the bend that makes layers useful.