Coding & Programming
Exploring new frameworks and building projects.
Matrix Coefficient
A coefficient matrix is a matrix formed by the coefficients of the variables in a system of linear equations, excluding the constant terms. Definition: A coefficient matrix is a matrix that contains the coefficients of the variables in a system of linear equations. Example: Consider the system of equa…
Magnitudes
The “magnitude” of a vector is the distance from the endpoint of the vector to the origin – in a word, it’s length.
Vector
A vector is an element in a vector space. It is a quantity that can describe both the direction and magnitude of an element. Matrices having a single row or column are referred to as vectors. A vector is a list of numbers. There are (at least) two ways to interpret what this list of numbers mean: One…
Linear Algebra
Linear algebra is mathematical discipline that deals with vectors and matrices and, more generally, with vector spaces and linear transformations Elementary linear algebra are given below: Scalars - A scalar is a quantity that only has magnitude and not direction. It is an element that is used to def…
Large Language Models (LLMs)
Large Language Models are a subset of neural networks designed specifically for processing and generating human language. They leverage vast amounts of text data to understand language nuances, context, and semantics. They rely on neural networks, particularly transformer architectures like GPT (Gen…
Breadth First Search (BFS) Algorithm
The Lee Algorithm is a breadth-first search (BFS) algorithm that is used to find the shortest path between two points in a grid-like structure, such as a maze. It is an unweighted grid-based algorithm, meaning that all cells in the grid have the same traversal cost, and it finds the shortest path …
Bellman-Ford Algorithm
The Bellman-Ford algorithm is a dynamic programming algorithm that computes the shortest paths from a single source vertex to all other vertices in a weighted graph. It is particularly useful for graphs that contain negative weight edges, which Dijkstra’s algorithm cannot handle. Key Characteristics…
Disjoint Set Union (DSU)
Union-Find, also known as the Disjoint Set Union (DSU), is a data structure that is used to manage a collection of disjoint (non-overlapping) sets. It supports two primary operations: Find: Determine the set to which a particular element belongs. Union: Merge two sets into a single set. The Union-Find…
Floyd-Warshall Algorithm
The Floyd-Warshall algorithm is a dynamic programming algorithm used to find the shortest paths between all pairs of vertices in a weighted graph. Unlike other algorithms such as Dijkstra’s, which computes the shortest path from a single source to all other vertices, the Floyd-Warshall algorithm co…