Lesson 2: Matrix Flashcards
A set of mn numbers (real or complex), arranged in a rectangular formation (array or table) having m rows and n columns and enclosed by a square bracket [ ] is called m n matrix (read “m by n matrix”) .
Matrix
The _________ or dimension of a matrix is the ordered pair having as first component the number of rows and as second component the number of columns in the matrix.
order
Some Types of Matrices
A matrix consisting of a single row is called a ___________ or a row vector.
row matrix
Some Types of Matrices
A matrix having single column is called a _________ or a column vector.
column matrix
Some Types of Matrices
A matrix in which each element is ‘0’ is called a ____ or Zero matrix. Zero matrices are generally denoted by the symbol O. This distinguishes zero matrix from the real number 0.
Null
Some Types of Matrices
A matrix A having same numbers of rows and columns is called a _________________. A matrix A of order m x n can be written as Amxn. If m = n, then the matrix is said to be a square matrix. A square matrix of order n x n, is simply written as An.
square matrix
Some Types of Matrices
The _________________ of a square matrix is the ordered set of elements aij, where i = j, extending from the upper left-hand corner to the lower right-hand corner of the matrix. Thus, the principal diagonal contains elements a11, a22, a33 etc.
principal diagonal
Some Types of Matrices
Particular cases of Square Matrix
A square matrix in which all elements are zero except those in the main or principal diagonal is called a __________________. Some elements of the principal diagonal may be zero but not all.
Diagonal matrix
Some Types of Matrices
Particular cases of Square Matrix
A diagonal matrix in which all the diagonal elements are same, is called a _________________.
Scalar matrix
Some Types of Matrices
Particular cases of Square Matrix
A scalar matrix in which each diagonal element is 1(unity) is called a ___________. An identity matrix of order n is denoted by _____.
Unit matrix, In
Some Types of Matrices
Particular cases of Square Matrix
Two matrices A and B are said to be equal if and only if they have the same order and each element of matrix A is equal to the corresponding element of matrix B i.e for each i, j, aij = bij.
Equal matrices
Some Types of Matrices
Particular cases of Square Matrix
The negative of the matrix Amxn, denoted by –Amxn, is the matrix formed by replacing each element in the matrix Amxn with its additive inverse.
Negative of a matrix
Operations on matrices
If A is a matrix and k is a scalar (constant), then kA is a matrix whose elements are the elements of A , each multiplied by k
Multiplication of a Matrix by a Scalar
Operations on matrices
If A and B are two matrices of same order m n then their sum A + B is defined as C, m n matrix such that each element of C is the sum of the corresponding elements of A and B .
Addition and subtraction of Matrices
Operations on matrices
Two matrices A and B are said to be conformable for the product AB if the number of columns of A is equal to the number of rows of B.
Product of Matrices
