Add Linear Algebra Documentation - Initial Vectors Section #10
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Create LinearAlgebra documentation section with four foundational topics: - 01 Vectors.md: Operations, magnitude, dot product, orthogonality, span - 02 Lines.md: Parametric, implicit, explicit forms; conversions; intersections - 03 Linear Transformations.md: Matrix representation, rotation, scaling, reflection, projection - 04 Matrices.md: Operations, determinant, inverse, eigenvalues, decompositions All files follow established documentation patterns: - MathWorld links for mathematical terms - Proper LaTeX formatting for equations - Cross-references between related topics - Applications sections
- Add 05 Systems of Equations.md covering algebraic methods (substitution, elimination), nonlinear systems, and solution types - Expand 04 Matrices.md with Cramer's rule example, matrix inverse method example, and detailed examples for infinitely many solutions and homogeneous systems - Update make.jl to include new Systems of Equations page - Minor updates to 01 Vectors.md
- Reorder definitions (algebraic first, then geometric) - Add Vector Notation section (column/row vectors, boldface, hat notation) - Add Components and Dimensions section - Fix typo in R^2 definition
- Add \[...\] delimiters to MathJax3 displayMath config (fixes literal \[ \] appearing) - Fix bullet points where LaTeX started immediately after dash (Unit Vectors, Polar Form, Key insights) - Update copilot-instructions.md with: - Enhanced bullet point rule with more examples - Absolute value notation (\lvert/\rvert) - Complete MathJax3 configuration section with migration instructions - Mark as canonical basis for other Julia Math repos
Vectors documentation: - Add section on generalizing vector operations to R^n - Include addition, scalar multiplication, subtraction formulas for n-dimensional vectors - Add notes on applications in data science and machine learning Basics notebook: - Add vector operation examples with production quantities - Add complex vector expression examples (v₁ - 4v₂ + 2v₃)
- Define basis vectors without using 'vector space' or 'linearly independent' - Show standard basis for R^2 and R^3 with concrete examples - Note connection between basis vectors and unit vectors - Fix L2 norm formatting
- Add documentation guideline: all terms must be defined before use - This principle drives document structure and section ordering - Refine 'Components and Dimensions' section to define space/R^n - Ensure logical progression throughout Vectors documentation
- Add Pythagorean derivation for magnitude formula - Explain extension to R^n via recursive Pythagorean theorem - Add trigonometric derivation for polar form - Explain normalization formula (why dividing by magnitude works) - Extend basis vectors explanation to R^n with summation notation
- Rearrange sections to follow 'define before use' principle - Add example to Basics notebook
- Add 10 new Geometry documents covering 2D/3D linear algebra: * Points and Coordinates (vectors, basis, barycentric coords) * Lines (parametric, implicit, explicit forms) * Dot Product and Orthogonality * Projections and Distance * Line Intersections * Transformations (rotation, reflection, projection, scaling) * Matrices and Maps (matrix-vector multiplication, determinants) * Linear Systems (Cramer's rule, Gaussian elimination) * Inverse and Kernel (invertibility, null space) * 3D Geometry (cross product, planes, 3D transformations) - Add 88 supporting images in Geometry/assets/ - Update make.jl with Geometry section in navigation - Add pagesonly=true to exclude source reference files - Update .gitignore to exclude Linear Algebra Capacities folder
Basics/01 Vectors: - Remove geometric concepts (magnitude, distance, basis vectors) - Keep algebraic definitions and properties - Add cross-references to Geometry section Geometry/01 Points and Coordinates: - Add position vector, free vector, displacement vector definitions - Add parallel vectors section - Add cross-reference to Basics for vector operations - Fix image paths
… content - Remove geometric interpretations from Basics/01 Vectors.md (parallelogram rule, scaling, linear independence) - Add Linear Independence (Geometric View) section to Geometry/01 Points and Coordinates.md - Update all cross-references to include specific section anchors - Add bidirectional links between algebraic and geometric sections
- Use correct capitalization in section anchors (e.g., #Coordinate-Independent-Operations) - Add document context to cross-references (e.g., 'in the Points and Coordinates document') - Document cross-reference syntax in copilot-instructions.md for future reference - Spaces in file paths use actual spaces, spaces in anchors use hyphens
- Delete Basics/02 Lines.md (content covered in Geometry section) - Add skew lines section to Geometry/10 3D Geometry.md - Renumber Basics files: 03→02, 04→03, 05→04 - Update make.jl pages array with new file names - Fix all cross-references to use updated file numbers
- Update index.md with source references (Farin & Hansford text) - Comment out all pages except 01 Vectors in make.jl for initial deploy - Comment out cross-references in 01 Vectors.md to excluded pages - Enables incremental review: deploy Vectors first, add more as reviewed
Symbolics.jl fix:
- Add fold=Val{true}() to substitute calls to force evaluation
- Add Float64.() wrapper to ensure numeric matrix types
- Fixes rtoldefault MethodError in isapprox comparisons
- All 68 tests now pass on Julia 1.12
index.md updates:
- Add detailed overview of package purpose and source materials
- Document source books for Basics and Geometry sections
- Minor grammar and clarity improvements
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Initial deployment of Linear Algebra documentation with coordinated Basics and Geometry sections.
Source Material:
This PR includes:
Incremental approach: Additional pages (02-10) are commented out pending review. They will be enabled in subsequent PRs.