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The article shares a candid interview anecdote about reasons for leaving a job, then presents LeetCode problem 542 “01 Matrix”, explains its DP and BFS approaches, and provides full Java, C++, and Python implementations.
This article explains how to represent, combine, and invert 2D and 3D transformations with matrices, demonstrates rotation around arbitrary axes, scaling in any direction, and provides JavaScript code for generating rotation matrices in WebGL contexts.
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Rotating a 2‑D vector is performed by multiplying it with the matrix [[cos θ, ‑sin θ],[sin θ, cos θ]], yielding the new coordinates (x cos θ ‑ y sin θ, x sin θ + y cos θ); a short JavaScript function implements this, turning [3,2] into [‑2,3] for a 90° counter‑clockwise rotation and also rotates the basis vectors.
This guide introduces NumPy fundamentals—including installation, array creation, indexing, slicing, universal functions, and linear‑algebra operations—providing concise code examples that demonstrate how to generate, manipulate, and compute with multidimensional arrays and matrices in Python.
This article explains how to compute determinants using cofactor expansion for 2×2 and 3×3 matrices, introduces the cofactor matrix, discusses properties of determinants, triangular matrix simplifications, and demonstrates Cramer's rule and an alternative inverse matrix method, providing clear examples throughout.
This article covers fundamental matrix concepts, including addition and multiplication properties, transpose rules, identity and elementary matrices, and practical algorithms for computing matrix inverses with illustrative examples.
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This article introduces NumPy, the essential Python library for array and matrix operations, covering creation, arithmetic, slicing, aggregation, reshaping, and real‑world examples such as machine‑learning data preparation, image handling, audio processing, and text tokenization.
The article analyzes how to update the positions of intermediate points on a wire when the user drags the wire with the mouse, compares three solution approaches—including point‑wise rotation and scaling, a complex geometric construction, and a unified transformation matrix—and summarizes their trade‑offs.
This article introduces the basic concepts of vectors and matrices, covering directed line segments, vector properties, coordinate representation, magnitude, inner product, Cauchy‑Schwarz inequality, and fundamental matrix operations such as addition, multiplication, Hadamard product and transposition, with examples and visual illustrations.
The article explains the mathematical foundations and front‑end implementation of five common mobile gestures—drag, pinch, rotate, single‑finger pinch, and single‑finger rotate—using native touch events, vector calculations, and matrix transformations, and provides a lightweight library that emits incremental gesture events for easy integration.