- matrix = rectangular array of numbers written between square brackets.
- dimension of a matrix = # of rows x # of columns
- vector = an n x 1 matrix where (n = # of rows)
- maxtrices are written with capital letters while vectors are written with lower case letters
- matrix matrix multiplication:
- A = [a b; c d; e f] which is a 3x2 matrix
- B = [g h i j; k l m n] which is a 2x4 matrix
- A * B = a 3x4 matrix
- To multiply A with B the # of columns in A must = # of rows in B.
- A * B = [ag+bk ah+bl ai+bm aj+bn; cg+dk ch+dl ci+dm cj+dn; eg+fk eh+fl ei+fm ej+fn]
- maxtrix properties: not commutative = matrix A x matrix B != B x A is associative = A x (B x C) = (A x B) x C
- identity matrix = I_nxn = has 1 along the top left to bottom right diagonal and 0 at every other element. For any matrix A_mxn * I_nxn = I_mxm * A_mxn = A_mxn
- Matrix inverses: Not all matrices have an inverse. Only a square matrix COULD have an inverse. A*A^-1 = A^-1 * A = I
- Matrix transpose: The transpose of a given matrix A_mxn is B_nxm where B_ij = A_ji.