addition, scalar multiplication, and transpose

column and row vectors

m x 1 and 1 x n matrices

cA is the matrix formed by

multiplying every entry in A by the scalar c

linear combinations of matrices and writing solutions to linear systems in parametric vector form

see notes

transpose of an m x n matrix is

an n x m matrix whose (j, i)-entry is the (i,j)-entry of the original

transpose properties

(A^T)^T = A

(cA)^T = c(A^T)

(A + B)^T = A^T + B^T

a SQUARE matrix is symmetric if

B^T = B (symmetry with respect to diagonal)