recs
23playlist
robot fartsdnb, amen breaks, csgo music
24playlist
cold hot coldchill, jazz, funk, not old music
25art
:^)faces i drew on microsoft paint, 250x250
26text
rowreduce melinear algebra notes i took from a DS textbook
linear algebra stuff works on things that are linear
basis vectors are the building blocks of vectors (it's like the squares in our 2d graph).
span is the space of the combinations that our vector can reach. sometimes your basis vectors can reach all available dimensions, sometimes not.
a matrix describes a transformation composed of its basis vectors. when you perform matrix-vector multiplication, you apply that transformation to the vector. matrix-matrix multiplication is just applying a transformation to another transformation. alternatively you can imagine matrix-vector multiplication as scaling the vector along the matrix's eigenvector by its eigenvalue (probably doesn't apply when eigenvalue is complex? idk???).
\(A\vec{v}=\lambda\vec{v}\)
\((A-\lambda I)\vec{v}=0\)
determinant describes how much your transformation (matrix) scales an area. Negative determinant means we invert ourselves, and a determinant of zero means we smash space to a lesser dimension (not necessarily one dimension down).
solve for \(\lambda\), \(det(A-\lambda I)=0\)
NOTE: discriminant is \(\sqrt{b^2-4ac}\)
Monoid: is a set, associative, has law of composition, and a unit element, represents a binary operation. e.g. \(S^2\mapsto S\)
27art
...in the subway, and cat, 500x500
