Vectors and Planes vs Linear Algebra Visualizer

Vectors and Planes App helps visualize and understand 3D linear and quadric structures and their intersections. List of linear structures and combinations: 1. Two vector combination. 2. Plane. 3. Line and plane combination. 4. Two plane combination. 5. Three plane combination. Current list of quadric structures: 1. Two sphere combination. 2. Standard ellipsoid. 3. Ellipsoid in a form of positive-definite matrix. 4. Standard cone. 5. Cone in a form of indefinite matrix. 6. 1-sheet hyperboloid. 7. 1-sheet hyperboloid in a form of indefinite matrix. 8. 2-sheet hyperboloid. 9. 2-sheet hyperboloid in a form of indefinite matrix. 10. Standard cylinder. 11. Cylinder in a form of positive-semidefinite matrix. 12. Hyperbolic paraboloid. 13. Elliptic paraboloid. Current list of combinations of quadric and linear structures: 1. Matrix ellipsoid and line. 2. Standard ellipsoid and plane. 3. Matrix ellipsoid and plane. 4. Matrix cone and line. 5. Standard cone and plane. 6. 1-sheet hyperboloid in matrix form and line. 7. 2-sheet hyperboloid in matrix form and line. 8. Matrix cylinder and line. 9. Elliptic paraboloid and line. 10. Hyperbolic paraboloid and line. Interactive 3D graphs are provided for all of the above. Step by step calculation algorithms are provided for all intersection point sets. Many of the algorithms are based on Linear Algebra concepts. Those, in turn, are explained in our “Matrix Solver Step by Step” app. Version 10 was completely redesigned. Developers hope to get feedback from users at graphmath@aol.com.

Ever wondered what a matrix is really doing? Whether you're learning it yourself or teaching students who are stuck, this app lets you visualise and manipulate matrix transformations, so you can finally see how and why they work. WHY IT CLICKS Most apps show you the answer. This one shows you why. The columns of a matrix are just where the basis vectors î and ĵ land. Column one is red. Column two is green. Follow those colors from your input, through the transformed vectors, into the step-by-step math. One number, traced all the way to its effect. With Linear Algebra Visualizer you: - Can finally build the visual intuition of linear algebra - Understand the math behind each transformation - Visually see why TRS order matters - Understand the effect of adding multiple matrices and translations - Watch eigenvectors and eigenvalues come alive BUILT FOR - Students surviving their first linear algebra course - Graphics programmers who want intuition, not just formulas - Teachers who need a live demo that lands - Anyone who's stared at a matrix and thought "but why does this work?" - Visual thinkers who've struggled to picture it all in their head Stop memorizing matrices. Start seeing them. Download Linear Algebra Vizualiser: Rotate, Scale, Shear, Reflect, Translate and learn to understand transformations visually. Ever wondered what a matrix is really doing? Whether you're learning it yourself or teaching students who are stuck, this app lets you visualise and manipulate matrix transformations, so you can finally see how and why they work. WHY IT CLICKS Most apps show you the answer. This one shows you why. The columns of a matrix are just where the basis vectors î and ĵ land. Column one is red. Column two is green. Follow those colours from your input, through the transformed vectors, into the step-by-step math. One number, traced all the way to its effect. With Linear Algebra Visualiser you: - Can finally build the visual intuition of linear algebra - Understand the math behind each transformation - Visually see why TRS order matters - Understand the effect of adding multiple matrices and translations - Watch eigenvectors and eigenvalues come alive BUILT FOR - Students surviving their first linear algebra course - Graphics programmers who want intuition, not just formulas - Teachers who need a live demo that lands - Anyone who's stared at a matrix and thought "but why does this work?" - Visual thinkers who've struggled to picture it all in their head Stop memorising matrices. Start seeing them. Download Linear Algebra Visualiser: Rotate, Scale, Shear, Reflect, Translate and learn to understand transformations visually. Terms of Use (EULA): https://www.apple.com/legal/internet-services/itunes/dev/stdeula/