External Presence

Selected GraphMath visualizations have been uploaded to Wikimedia Commons and incorporated into specific sections of Wikipedia articles.

Wikipedia article section	Wikimedia Commons file
Gaussian elimination — Definitions and example of algorithm Row reduction interpreted as multiplication by elementary matrices.	Gaussian elimination as multiplication by elementary matrices
Gaussian elimination — Row operations Row reduction interpreted as changes in the row normal planes under multiplication by elementary matrices.	Gaussian elimination as multiplication by elementary matrices - row view
System of linear equations — Row reduction Animated row-normal-plane view of row reduction for a linear system.	Row reduction of a linear system - row normal planes animation
System of linear equations — Consistency Animated row-normal-plane view of two inconsistent systems of three linear equations.	Two inconsistent systems of three linear equations - row normal planes animation
Gaussian elimination Animated row-normal-plane view of Gaussian elimination for a system with infinitely many solutions.	Gaussian elimination of a linear system with infinitely many solutions - row normal planes animation
Shear mapping — Higher dimensions Animated 3D example of elementary shear of x by y.	3D elementary shear of x by y
Change of basis Coordinate change between the standard basis and a new basis.	Change-of-basis coordinate mapping (matrix representation)
Change of basis Coordinate transformation between two non-standard bases.	Change of basis — coordinate transformation between bases
Determinant Determinant as signed volume under multiplication by elementary matrices.	Determinant as signed volume under multiplication by elementary matrices
Laplace expansion — Proof Recursive view of Laplace expansion as determinant permutation lists in the 3×3 case.	Laplace expansion as recursive determinant permutation lists - 3 by 3 case
Cramer's rule — Geometric interpretation Determinant ratio in 3D visualized geometrically.	Cramers rule determinant ratio in 3D animation
Row and column spaces — Relation to the left null space Diagram of the four fundamental subspaces.	Four fundamental subspaces of a matrix (diagram)
Projection (linear algebra) — Orthogonal projections Projection onto a subspace shown geometrically.	Least squares projection geometry
Projection (linear algebra) — Finding projection with an inner product Projection using orthonormal basis and inner products.	Orthogonal projection using an orthonormal basis
Reflection (mathematics) — Reflection through a hyperplane in n dimensions Animated reflection across a plane in ℝ³ using a projection matrix.	Reflection across a plane in R3 using a projection matrix
Rodrigues' rotation formula — Derivation Animation of vector rotation around an axis using Rodrigues' rotation formula.	Rodrigues rotation formula animation
Rodrigues' rotation formula — Matrix notation Step-by-step geometric construction of Rodrigues' rotation formula.	Rodrigues rotation formula steps diagram
Axis–angle representation — Example Animated cube rotation illustrating axis–angle representation.	Axis-angle representation of a cube rotation
QR decomposition — Square matrix Gram-Schmidt orthogonalization and upper-triangular structure.	QR decomposition geometric interpretation (2D)
QR decomposition — Example 3D geometric interpretation of QR factorization.	QR decomposition geometric interpretation (3D)
Givens rotation — Triangularization Stepwise triangularization by Givens rotations.	Givens rotation triangularization - stepwise animation
Ordinary least squares — Projection Least squares as projection onto the column space.	Geometric interpretation of least squares (three observations)
Diagonalizable matrix — Diagonalizable matrices Orthogonal diagonalization of a real symmetric matrix as a change to an orthonormal eigenvector basis, diagonal scaling and transformation back.	Orthogonal diagonalization of a real symmetric matrix
Geometric visualizations of orthogonal diagonalization An orthogonal projection matrix diagonalized in an orthonormal eigenvector basis, with eigenvalues 1 and 0.	Orthogonal diagonalization of an orthogonal projection matrix
Geometric visualizations of orthogonal diagonalization A reflection matrix diagonalized in an orthonormal eigenvector basis, with eigenvalues 1 and −1.	Orthogonal diagonalization of a reflection matrix
Eigenvalues and eigenvectors — Overview Animated examples of non-symmetric 2D transformations with real eigenvalues and their eigenvector directions.	Eigenvectors of various non-symmetric 2D transformations with real eigenvalues - animation
Geometric visualizations of eigenvectors and eigenvalues in two dimensions Animated 2D transformations with complex eigenvalues, showing the absence of real invariant directions.	2D linear transformations with complex eigenvalues - animation
Geometric visualizations of eigenvectors and eigenvalues in two dimensions Animated symmetric 2D transformations with positive, negative and mixed-sign eigenvalues.	Symmetric 2D transformations with positive, negative and mixed-sign eigenvalues - animation

Eteri Byazrova on Wikimedia Commons
GraphMath diagrams, animations and other visual contributions uploaded to Wikimedia Commons.

Eteri Byazrova on Wikipedia
Wikipedia user page associated with GraphMath contributions.

Selected GraphMath contributions to Mathematics Stack Exchange and Computational Science Stack Exchange.

Are orientation-preserving QR transformations useful in computational applications?
Computational Science Stack Exchange question on orientation-preserving QR transformations and their possible practical uses.

QR decomposition interpretation
Mathematics Stack Exchange answer comparing geometric interpretations of Gram-Schmidt, Givens rotations, Householder reflections and direct rotations.

How does Cramer's rule work?
Mathematics Stack Exchange answer giving a geometric interpretation of Cramer's rule using determinant ratios.

Geometric intuition for the Householder transformation
Mathematics Stack Exchange answer illustrating the geometric action of a Householder reflection.

GraphMath materials are also available through public repositories and long-term archives.

GitHub repository
Source materials, diagrams and structured content are published in a public repository.

Zenodo DOI archive
Selected GraphMath materials are archived on Zenodo for long-term access and citation.

Geometric Interpretation of Least Squares (OLS): Projection onto Column Space

Cross Product: A Geometric Derivation from Area, Orientation and Orthogonality

QR Factorization Through Direct Plane Rotations

Selected GraphMath materials are also listed on public educational platforms.

OER Commons
Public open educational resource listings for selected GraphMath chapters.

Geometric Interpretation of Least Squares (OLS)

Four Fundamental Subspaces of a Matrix

3D Rotation Around an Axis (Rodrigues Formula)

Cross Product — A Geometric Derivation

MERLOT materials
Public MERLOT listing for GraphMath Linear Algebra educational resources.

Selected GraphMath articles are also available on Medium.

GraphMath on Medium
GraphMath publication for articles and essays on linear algebra and geometric explanation.

Why changing a regression model changes the projection
Article on how model changes alter the projection in least squares geometry.