Null Matrix or Zero Matrix
A matrix of order m x n whose elements are all 0 is called a null matrix (or zero matrix) of order m x n. It is usually denoted by O or more clearly [O] m , n..
Definition of a Matrix
Matrices - Consider the arrangement In this arrangement, there are two rows and four columns. The number 3 lies in the 2 n d row and 4 t h column. Each number has a fixed position. Matrix A has 2 rows and 3 columns and is thus of order 2 x 3. Matrix B has 3 rows and 2 columns an..
Matrices - Consider the arrangement In this arrangement, there are two rows and four columns. The number 3 lies in the 2 n d row and 4 t h column. Each number has a fixed position. Matrix A has 2 rows and 3 columns and is thus of order 2 x 3. Matrix B has 3 rows and 2 columns an..Row Matrix
A matrix having only one row is called a row-matrix. For example: A[1 3 2 -2] is a row matrix of order 1 x..
Column Matrix
A matrix having only one column is called a column matrix. 3 x 1 and 4 x 1 respectivel..
A matrix having only one column is called a column matrix. 3 x 1 and 4 x 1 respectivel..Diagonal Matrix
A square matrix A=[a i j ] n x n is called a diagonal matrix if all the elements, except those in the leading diagonal, are zero. i.e., a i j = 0 for all i ..
A square matrix A=[a i j ] n x n is called a diagonal matrix if all the elements, except those in the leading diagonal, are zero. i.e., a i j = 0 for all i ..Symmetric Matrix
A square matrix A = [a i j ] is said to be symmetric if its (i,j) t h element is the same as its (j,i) t h element. i.e a i j = a j i " i, j A square matrix A is said to be symmetric, if A = A ..
A square matrix A = [a i j ] is said to be symmetric if its (i,j) t h element is the same as its (j,i) t h element. i.e a i j = a j i " i, j A square matrix A is said to be symmetric, if A = A ..Inverse of a Square Matrix
Let A be a square matrix of order n. If there exists a matrix B of order n such that AB = BA = I, where I is the identity matrix of order n, then the matrix A is said to be invertible and B is called the inverse (or reciprocal) of ..
Identity or Unit Matrix
A square matrix A=[a i j ] n x n is called an identity or unit matrix if (2) a i j =1 for all i = j In other words a square matrix each of whose diagonal elements is unity and each of whose non-diagonal elements is equal to zero is called an identity or unit h..
A square matrix A=[a i j ] n x n is called an identity or unit matrix if (2) a i j =1 for all i = j In other words a square matrix each of whose diagonal elements is unity and each of whose non-diagonal elements is equal to zero is called an identity or unit h..Adjoint of a Square Matrix
The adjoint of a square matrix [a i j ] is defined as the transpose of the matrix [A i j ] where A i j are the cofactors of the elements a i j . Adjoint of A is denoted by adj A. ..
The adjoint of a square matrix [a i j ] is defined as the transpose of the matrix [A i j ] where A i j are the cofactors of the elements a i j . Adjoint of A is denoted by adj A. ..Properties of Inverse of Matrix
In other words, a square matrix A is invertible if and only if A is a non-singular matrix. (c) If A and B are invertible square matrices, then (AB) - 1 = B - 1 A - 1 (d) If A and B are two non-singular square matrices of the same order, then AB and BA are also non-sin..
In other words, a square matrix A is invertible if and only if A is a non-singular matrix. (c) If A and B are invertible square matrices, then (AB) - 1 = B - 1 A - 1 (d) If A and B are two non-singular square matrices of the same order, then AB and BA are also non-sin..See what our Users say :
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