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Section 4.2 Terminology and notation
\(\nth[(i,j)]\) entry of a matrix
the entry in the \(\nth[i]\) row and \(\nth[j]\) column of a matrix
size (or dimensions) of a matrix
the number of rows and columns in a matrix, usually written \(m \times n\) to mean \(m\) rows and \(n\) columns
equal matrices
matrices with the same size, and the same numbers in corresponding entries
matrix addition
the new matrix obtained from two old matrices of identical sizes by adding corresponding entries
scalar multiple
the new matrix obtained from an old matrix obtained by multiplying every entry by the same number \(k\text{;}\) the common scale factor \(k\) is called a scalar
zero matrix
a matrix where every entry is zero, written \(\zerovec\)
column vector
a matrix consisting of a single column
row vector
a matrix consisting of a single row
vector of unknowns
a column vector containing all of the variables in a system
vector of constants
a column vector containing all of the constants from the right-hand sides of the equations in a system
square matrix
a matrix with the same number of columns as rows
main diagonal
the diagonal of entries in a square matrix from top left to bottom right
transpose
the new matrix obtained from an old matrix by turning rows into columns and columns into rows; we usually write \(\utrans{A}\) to mean the transpose of the matrix \(A\)
