Linear Algebra
Linear Algebra 1:
Matrix manipulations, lots of higher dimensional thinking, not proof based. I found this course more intuitive than Calculus. Linear dependence, vectors, matrices, determinants, etc.
Common Symbols in LA:
ℝ = All real numbers (integers, rational, irrational)
ℝn = n denotes the dimension we are in
ℝ2 is the cartesian plane (x,y) aka 2D space
ℝ3 is in 3 dimensional space (x,y,z)
Let A denote a matrix:
| A | or det(A) = The determinant of Matrix A
I = The identity matrix
E = The elementary matrix
Eij = i denotes the # of rows in the matrix, and j denotes the # of columns
Mmxn = All matricies with m rows and n columns
A-1 = The inverse matrix of A
AT = The transpose matrix of A
sp(A) or span(A) = The span of A (set of all linear combinations of the vectors/matrices)
dim(A) = The dimension of A
col(A) = Column space of A (span of its column vectors)
row(A) = Row space of A (span of its column vectors)
rank(A) = The rank of A (dimension of row space)
adj(A) = Adjugate matrix (transpose of cofactor matrix)
Let A,B denote 2 vectors
→ A = A is a vector
|| A || = The norm of A
A X B = The cross product of A and B (only defined in the 3rd Dimension)
A * B or A . B = The dot product (inner product) of A and B (scalar)
A ⊂ B = A is a subset of B
3rd party resources:
Defining a Plane using a Normal Vector and a Point