Linear Algebra Symbols

{A}

Set A

Set is always denoted by a capital letter in curly bracket

If set A is set of even numbers then

{A} = {2, 4, 6, 8…}

⊂

Subset

Subset means all element of a set is member of another set

Natural Number is subset of integers as all the members of natural numbers are memeber of integers

⊃

Superset

Superset means the set on left side of symbol has all the members of another set

Integeer is superset of Natural Number

⋃

Union of Set

It means combining elements of two sets whiling keeping the common elements only once

A = {2, 3, 4}, B = {2, 4, 6}

Then A ⋃ B = {2, 3, 4, 6}

⋂

Intersection of Set

Intersection of sets means fidning out common elements between two sets

A = {2, 3, 4}, B = {2, 4, 6}

Then A ⋂ B = {2, 4}

n(A)

Cardinality of Set

It denotes the number of elements in a given set

A = {2, 4, 6} then n(A) = 3

Φ

Null Set

Null set means there is no element in that set

Set of Natural Number greater than 2 but less than 3

A_ij

Matrices

Matrix is represented by Capital letters, matrices are arrays of numbers, symbols or expressions

[Tex]A_{3\times2} = \begin{bmatrix} 1& 2\\ 3& 4\\ 5& 6\\ \end{bmatrix} [/Tex]

| A | or det(A)

Determinant

It represents the Determinant of a square matrix A.

If we have matrix A = [Tex] \begin{bmatrix} 1& 2\\ 3& 4\\ \end{bmatrix} [/Tex] then

|A| = |1 × 4 – 2 ×3| = 4 – 6 = -2

A^T

Tanspose of Matrix

In Transpose of Matrix, the elements of rows are arranged in column and vice versa

If we have matrix A = [Tex] \begin{bmatrix} 1& 2\\ 3& 4\\ \end{bmatrix} [/Tex] then

A^T = [Tex] \begin{bmatrix} 1& 3\\ 2& 4\\ \end{bmatrix} [/Tex]

A^-1

Inverse of Matrix

Inverse of Matrix basically means finding a matrix that when multiplied to orginal matrix give

For Matrix A = [Tex] \begin{bmatrix} 1& 2\\ 3& 4\\ \end{bmatrix} [/Tex]

A^-1 = [Tex] \begin{bmatrix} -2& 1\\ 3/2& -1/2\\ \end{bmatrix} [/Tex]