Scalar Number
Single number.
Vector
Array of numbers.
Matrix
2d array of numbers (A[i:] is the i’th row, A[:j] is the j’th column).
Tensor
Array with more than two axes (A_i,j,k for example).
Transpose
Mirror of vector/matrix
Linear Transformation
A function from one vector space to another that respects the underlying (linear) structure of each vector space.
A_x = B
Identity Matrix
1 for every n=n.
Inverse
A -> A^-1
Norms
Used for measuring the size of a vector.
L^p Norm
The equation that’s used to measure the size of a vector.
||x||p = ( ∑i|x_i|p)^1/p
L^2 Norm
||x||2 = ( ∑i|x_i|p)^1/p = √ ∑i|x_i|^2
L^1 Norm
||x|| = ∑i|x_i|
L^∞
||x||∞ = max_i |x_i |