[칸 아카데미] 선형대수학

vector : magnitude & directionR space : real coordinate space=> all possible real value 2-tuple=> It means a list which has ordervector addition => It

There are v1, v2, ... vn vectors in real Ndim space, when we can combine const \* vec all of it (const is also in real Ndim space), it calls linear co

When the spanning (vec v1, vec v2) is colinear!It can not represent the other dimensions by using linear combinationNot only spanning (vec v1, vec v2)

V is a subset of real spaceIf x vector is in V, cx vec is also in there closure under scalar multiplicationElse if a vec and b vec are in V, a+b vec i

Both of them, scalar!Commutative & Associative & DistributiveConstant c is a positive!Using by law of cosine and triangle propertiesWe can represent t

When dot product is a scalar, cross product is a vector which is only defined in R3.It's impossible in a R4 or greater!The cross product vector of ve

[칸 아카데미] 선형대수학

Let's define Ax, A is a matrix and x is a vector.If we have A matrix shaped m by n, and x vector shaped n by 1, we can define b vector shaped m by 1.E

What is the column space?If you have the matrix A which size is m by n, you can span the subspace by using n vectors of column sets.Matrix is the just

If you have a matrix B, let's get the Null space of B.You've got right now that the vectors are in a 5 dimension of real space.And we already know abo