Equality of two matrices

Two matrices are said to be equal if and only if they have the same order and the corresponding elements are equal.

Transpose of a matrix

The matrix obtained by interchanging the rows to columns and columns to rows is called transpose of that matrix.

Matrix - Square, Scalar, Symmetric, Skew symmetric

Square matrix
If the number of rows and columns are equal then the matrix is called a square matrix.

Scalar Matrix
A square matrix in which all the elements in the main diagonal are equal and the rest of the elements are zero.

Symmetric Matrix
If the transpose of matrix is equal to matrix itself then the matrix is called symmetric matrix.

Skew symmetric matrix
If the transpose of a matrix is equal to the additive inverse of the given matrix then the given matrix is called skew symmetric matrix.

Unity or Identity Matrix

A square matrix whose main diagonal elements are all unity and the other elements are zero is called a unity or identity matrix.

Null Matrix

A matrix of any order whose all elements are zero is called a null matrix.

Column Matrix

If there is only one column in a matrix, it is called column matrix.

Rectangular matrix & Row matrix

Rectangular matrix
If the number of rows is not equal to the number of columns then the matrix is called a rectangular matrix.

Row matrix
If there is only one row in a matrix, it is called row matrix.

Perfect number

A number for which the sum of all its factors is twice the number itself is called a perfect number.

Matrix

A matrix is a rectangular array of numbers enclosed by a pair of brackets.

Proportion

The equality of two ratios is called a proportion.

Ratio

If two quantities expressed in the same units are compared by division the result obtained is called a ratio.

Triangle

A closed figure with three sides is called a triangle
or
Area formed by joining three points not lying on a line.

Obtuse angled triangle

A triangle in which one of the angle is an obtuse (one angle > 90 degree) is called an obtuse angled triangle.

Acute angled triangle

A triangle in which all the three angles are acute is called an acute angled triangle.

Right angled triangle

A triangle in which one of the angle is a right angle (90 degree) is called a right angled triangle.

Scalene triangle

A triangle in which no two sides are equal is called a scalene triangle.

Isosceles triangle

A triangle is said to be isosceles triangle if and only if its any two sides are equal and different from third side.

Equilateral triangle

A triangle is said to be equilateral triangle if and only if all the sides  are equal to each other.
or
A triangle is said to be equilateral triangle if its ll the three vertices are equidistant from each other.

Congruent

If two quantities have the same shape and size then these two quantities are said to be congruent to each other

Diagonal of a polygon

 The line which joins two non-consecutive vertices is known as diagonal of a polygon.