Algebra Archives - PostNetwork Academy

Some Questions of Linear Algebra: Linear Transformation

Some Questions of Linear Algebra: Linear Transformation Definition: Linear Transformation A linear transformation $T: \mathbb{R}^n \to \mathbb{R}^m$ is a function that satisfies: Additivity: $T(\mathbf{u} + \mathbf{v}) = T(\mathbf{u}) + T(\mathbf{v})$ for all $\mathbf{u}, \mathbf{v} \in \mathbb{R}^n$. Homogeneity: $T(c \mathbf{v}) = c T(\mathbf{v})$ for all $\mathbf{v} \in \mathbb{R}^n$ and scalars $c$. Numerical Example: Linear Transformation […]

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Addition Law of Probability and Examples

Algebra, Artificial Intelligence, Data Handling, Research and Development, Statistics / Bindeshwar S. Kushwaha

Addition Law of Probability and Examples Data Science and A.I. Lecture Series Introduction to Addition Law Statement: For any two events $ A $ and $ B $, the probability of their union is given by: \[ P(A \cup B) = P(A) + P(B) – P(A \cap B) \] This formula calculates the probability

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Set Operations and Important Laws

Algebra, Artificial Intelligence, Machine Learning, Mathematics, Maths, Probability and Statistics, Statistics / Bindeshwar S. Kushwaha

Set Operations and Important Laws Data Science and A.I. Lecture Series Set Operations Union Definition: \[ A \cup B = \{x : x \in A \text{ or } x \in B\} \] Examples: \( A = \{1, 2, 3\}, B = \{3, 4, 5\} \implies A \cup B = \{1, 2, 3, 4, 5\}

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Venn Diagrams

Algebra, Artificial Intelligence, Research and Development, Statistics / Bindeshwar S. Kushwaha

Venn Diagrams – Data Science and AI Lecture Series Welcome to our Data Science and AI Lecture Series! In this post, we’ll dive into the world of Venn Diagrams, an essential tool in set theory that simplifies understanding the relationships between sets. Whether you’re studying mathematics, data science, or AI, mastering concepts like intersections, unions,

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Hierarchy of Sets

Algebra, Artificial Intelligence, Data Handling, Statistics / Bindeshwar S. Kushwaha

& Hierarchy of Sets Universal Set ($ U $) The universal set ($ U $) contains all elements under consideration in a specific context. Example 1: If studying numbers, $ U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} $. Example 2: If studying letters, \( U = \{\text{a, b, c, …,

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Understanding Permutations

Algebra, Artificial Intelligence, Counting Principle, Machine Learning, Mathematics, Permutations and Combinations, Probability and Statistics, Statistics / Bindeshwar S. Kushwaha

Understanding Permutations Data Science and A.I. Lecture Series Author: Bindeshwar Singh Kushwaha PostNetwork Academy Introduction to Permutations A permutation is an arrangement of objects in a specific order. The order of arrangement is crucial in permutations. Example: Arranging the letters of the word “ABC”. Total permutations = $3! = 6$. Key Formula for Permutations The

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Group in Algebra

Leave a Comment / Algebra, Maths / Bindeshwar S. Kushwaha

Group in Algebra Let G be a non-empty set and * (multiplication) be a binary operation defined on G. Then algebraic structure (G, *) is called group if it satisfies the following axioms. 1- Closure property If a∈G, and b∈G then a*b∈G it is called closure property. of G 2- Associativity If a∈G, b∈G ,

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Algebra