English series
AI
English editions of Guozhen AI articles. The text is localized for global readers while the original diagrams, screenshots, and code examples remain aligned with the Chinese source.
Use this series as the technical reading layer, then continue into AI software buyer guides, tool comparisons, benchmarks, API platform decisions, coding agents, and LLM security research.
From Series Reading to Tool Decisions
Turn this AI series into practical software, model, API, and security choices.
English Series FAQ
Use this series as evidence before choosing AI tools.
How should I use the AI English series?
Use the series as the learning layer for concepts, screenshots, prompts, and implementation details, then continue into buyer guides, tool comparisons, benchmarks, API decisions, and security checks.
Is the AI series enough to choose an AI tool?
No. The series gives context and practical examples, but production choices still need pricing review, privacy checks, integration testing, benchmark evidence, and fallback planning.
What should I read after this 26-lesson series?
Open AI Software Buyer Guides, AI Tools Workbench, Best AI Coding Agents, AI Model Benchmarks, OpenAI vs Anthropic API, or LLM Security Tools depending on your next decision.
Why keep the original diagrams and screenshots?
The visuals preserve source evidence from the Chinese articles, so global readers can inspect interfaces, outputs, and workflows instead of relying only on a translated summary.
Assume we have historical stock price data
State space models describe how a system evolves over time using matrices. They unify historical states, external inputs, and observed outputs within a single linear...
Read lessonActivation function
At its core, neural network computation still consists largely of matrix multiplications. Understanding tensor shapes, weights, and gradients transforms deep learnin...
Read lessonGenerate sample data
Machine learning training is commonly expressed in matrix form: a batch of samples is processed simultaneously to compute predictions, followed by parameter updates...
Read lessonLoad image
The core idea behind SVD applications is to preserve dominant structural components while discarding weak, noisy ones. Image compression, recommendation systems, and...
Read lessonDefine matrix A
You can compute singular values manually by starting from the eigenvalues of $A^T A$. In practice, engineers delegate this task to numerical libraries—but understand...
Read lessonGenerate a simple random matrix (imagine it as a grayscale image)
SVD decomposes any matrix into three components: direction, magnitude (strength), and direction again. It is more general than eigenvalue decomposition and better su...
Read lessonExtract TF-IDF vectors for the first and second documents
Inner product spaces bring geometric notions—such as distance, angle, and projection—into algorithmic design. Recommendation systems, search engines, and regression...
Read lessonExample vectors
An orthogonal basis functions like a set of mutually independent coordinate rulers. When representing vectors using such a basis, projections and reconstructions bec...
Read lessonDefine vectors
The inner product compresses the relationship between two vectors into a single scalar. It simultaneously connects vector length, angle between vectors, and similari...
Read lessonDefine matrix A
Eigen decomposition breaks down a complex matrix into two intuitive components: direction (encoded in eigenvectors) and scaling (encoded in eigenvalues). When applic...
Read lesson16. Eigenvectors: Definition and Intuition
An eigenvector is not a fixed length arrow—it is a direction . As long as the direction remains unchanged, scalar multiples of the same vector still represent the sa...
Read lessonDefine the matrix
Eigenvalues quantify how much a matrix scales vectors along certain special directions. They serve as a crucial entry point for understanding dimensionality reductio...
Read lessonDefine coefficient matrix A
A homogeneous system always has the trivial (zero) solution. For a nonhomogeneous system, we must first determine whether a solution exists. If a solution exists, th...
Read lesson13. Gaussian Elimination for Systems of Linear Equations
Gaussian elimination fundamentally simplifies a system of linear equations using equivalent transformations —operations that preserve the solution set while progress...
Read lessonDefine coefficient matrix and constant vector
A linear equation describes a constraint—on a line, a plane, or in higher dimensional space. When multiple such constraints are combined, they form a system of equat...
Read lessonDefine a 3×3 matrix
When computing determinants, low order matrices can be expanded directly; for higher order matrices, it’s more efficient to use row operations to convert the matrix...
Read lesson10 Properties of Determinants
Determinant properties exist to enable faster, more robust computation—and also help determine whether a matrix is singular (degenerate) or whether a linear transfor...
Read lessonDeterminants: Definition and Intuition
A determinant can be understood as the scaling factor by which a linear transformation changes the volume of space. When the determinant equals zero, space is flatte...
Read lessonMatrix Transposition and Inversion
Transposition is commonly used to adjust orientation and compute inner products; the inverse matrix represents the transformation that “undoes” the original one. In...
Read lessonMatrix Multiplication and Its Properties
Matrix multiplication is not element wise multiplication—it computes dot products between rows and columns. It models feature weighting, coordinate transformations,...
Read lessonLinear Algebra for AI: Matrix Addition and Scalar Multiplication
Matrix addition and scalar multiplication may appear simple at first glance—but they form the foundational starting point for understanding batch feature updates, we...
Read lessonVector and Matrix Operations
Behind every operation rule lies meaning: addition represents composition, scalar multiplication represents scaling, the dot product measures similarity, and matrix...
Read lessonCreate a 2-row, 3-column matrix
I always write down the matrix shape explicitly first. Confusing rows and columns will lead to errors in subsequent matrix multiplication and model input. In the pre...
Read lessonSimulated pixel values (0–255) for an image
A vector can represent either a geometric arrow or a row of features. When reading AI code, it is far more common to convert samples into feature vectors.
Read lessonGenerate synthetic data
Many computations in AI can be expressed in terms of linear algebra: inputs are vectors, parameters are matrices, and training amounts to finding better directions i...
Read lesson1. Introduction to Linear Algebra: Core Concepts
Don’t rush to memorize formulas when learning linear algebra. Instead, think of vectors as data , matrices as transformations , and systems of equations as constrain...
Read lesson