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
Remark 4.2.1.
We will encounter the geometric origin of the word scalar in Chapter 12.
- 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 \(A\)