All Matrix's Definations for SY-BCA

1. Matrix: 

A matrix is an arrangement of numbers with M rows and N columns in a rectangular array.
Matrices are denoted by capital letter. like A,B,C

2. Raw Matrix:

A matrix in which there is only one rows and any number of columns this called a row matrix.

3. Column Matrix:

A matrix in which there is only one column and any number of row this called a column matrix.

4. Equal Matrices:

Two  Matrices A and B are called equal  matrices if the following two condition are satisfied.
 (1) Order of both the  matrices must be same.
 (2) Corresponding elements of both the  matrices must be same.

5.  Null Matrix:

A matrix whose all the elements are zero it’s called an empty matrix or null matrix.

 

6. Unit Matrix:

A matrix in which all the principal diagonal elements are one and all other are zero is called an identity matrix / unit matrix.
It is denoted by I.

7. Diagonal Matrix :

A square matrix in which all the elements except principle diagonal elements are zero is called a diagonal matrix.

8. Scalar Matrix:

A square matrix in which all the principle diagonal elements are same and all other are zero is called scalar matrix.

 

9. Symmetric Matrix:

If for any square matrix A, AT = A than A is said to be symmetric matrix.

10 Skew-Symmetric:

If for any square matrix A. AT = -A then A is said to be skew-symmetric matrix.

 

11. Triangular Matrix:

A square matrix in which all the elements above/below principle diagonal elements are zero is called triangular matrix.

12. Transpose of Matrix:

A matrix which is obtained by interchanging rows into columns or columns into rows is called transpose of a given matrix.

13 Inverse Matrix:

If for any matrix A, there exist a matrix B such that AB=BA=I. B is called inverse of A.

14. Singular Matrix:

 A square matrix A is said to be a singular matrix if it’s determinant is zero.

15 Non-Singular Matrix:

A square matrix A is said to be a non - singular matrix if it’s determinant is non zero.

16. Orthogonal Matrix:

A square matrix A is said to be an orthogonal matrix if A.AT = AT.A=I

17. Involuntary Matrix:

A square matrix A is said to be an involuntary matrix if A2=I.
Given matrix is involuntary matrix for any value of x.

18 Square Matrix:

A square matrix A is said to be idempotent matrix if A2=A.

19 Rank of Matrix:
A matrix is said to be of rank r, if the following to condition are satisfied.

1) It has at least one non zero determinant(minor) of a order r.
2) every determinant of order higher than r becomes zero.