Matrices and Vectors

R symbol

all real numbers, also known as scalar

E symbol

denotes membership

scalar

a single numerical quantity, also known as real number

vector in Rn

list of n scalars organized vertically into a list

coordinates

scalars in a vector

m x n matrix

matrix with m rows and n columns

transposition

interchanging the rows and columns of a matrix

linear operation

a mathematical function that preserves addition and scaling

involution

an operator that if applied twice it returns the matrix to the original

symmetric

matrix whose transpose is the same as the original

square

matrix that has the same number of rows and columns

trace

sum of the diagonal

upper triangular

every entry below the diagonal is equal to zero

lower triangular

every entry above the diagonal is equal to zero

diagonal matrix

if all non-diagonal entries are zero

zero matrix

matrix with all zeroes

nonzero matrix

matrix with at least one nonzero entry

nxn identity matrix

matrix with ones on the diagonal and zeros everywhere else

first pivot column

first nonzero column of a matrix

rank one matrix

every column of the matrix is a scalar multiple of the first column