| Title | Description |
|---|---|
| Examples of Linear Transformations | An applet that allows users to select linear transformations, view the image of a region of the coordinate plane under their composition, and challenges users to find transformations that map a region exactly to itself. |
| Eigenvectors | An applet the shows the effect of applying a linear transformation, input by the user, to a chosen number of unit vectors. Eigenvectors are also shown to illustrates how they are unchanged by the linear transformation. |
| Transformer3D | An applet that allows users to see a visual representation of the effect of a linear trasnformation on a region in a 3-dimensional coordinate space. |
| Eigenvalues and Eigenvectors | An applet that allows users to view the eigenvalues and eigenvectors of a given linear transformation, as well as visualize eigenspaces. |
| The Transformation Matrix and its Determinant | An applet that allows users to drag an image, distorting it and providing a matrix that transformations the image to the state created by the user. |
| Title | Description |
|---|---|
| Indian Institute of Technology Bombay - Mathematics Resource Center | A collection of applets for use in a linear algebra classroom. Concepts are situated in a geometric context, potentially augmenting students' capacity for visualization. |
| Mercyhurst University - Applets by Dr. Lauren Williams | A collection of applets for a wide variety of mathematical disciplines. These use Javascript and HTML and function on new browsers. |
| Conceptual Online Linear Algebra | A collection of applets (and other resources) focused entirely on helping students gain a conceptual understanding of linear algebra topics. |
| Terence Tao Java Applets | A collection of applets that cover a broad range of topics. Also included is a number of applets specfically related to linear algebra topics that were created by Kim Chi Tran. |
| Digital Mathematics | A collection of applets for exploring geometry, trigonometry, calculus, statistics, and, most importantly for the purposes of this site, linear algebra. |
| Source | Title | Citation |
|---|---|---|
| Book | Linear Algebra Done Right | Axler, S. (2017). Linear Algebra Done Right. Place of publication not identified: Springer. |
| Book | The Theory of Linear Algebra | Beasley, L. B. (2011). The Theory of Linear Algebra. Logan, UT: Utah State University. |
| Book | Matrices and Linear Transformations | Cullen, C. G. (1990). Matrices and Linear Transformations. New York: Dover. |
| Book | Linear Algebra | Friedberg, S. H., Insel, A. J., & Spence, L. E. (2003). Linear algebra (4th ed.). Upper Saddle River, New Jersey: Pearson Education. |
| Book | The Linear Algebra a Beginning Graduate Student Ought To Know | Golan, J. S. (2012). The Linear Algebra a Beginning Graduate Student Ought to Know. Dordrecht: Springer. |
| Journal Article | Transformations of Interval Linear Systems of Equations and Inequalities | HladÃk, M. (2016). Transformations of interval linear systems of equations and inequalities. Linear and Multilinear Algebra, 65(2), 211-223. doi:10.1080/03081087.2016.1180339 |
| Book | Algebra | Hungerford, T. W. (1974). Algebra. New York: Rinehart and Winston. |
| Journal Article | Trace Preserving Linear Transformtions on Matrix Algebras | Kovascs, A. (1977). Trace preserving linear transformations on matrix algebras. Linear and Multilinear Algebra, 4(4), 243-250. doi:10.1080/03081087708817158 |
| Book | Linear Algebra | Lang, S. (2000). Linear Algebra. New York: Springer. |
| Book | Linear Algebra With Applications | Leon, S. J. (2010). Linear Algebra With Applications. Upper Saddle River, NJ: Pearson Education International. |
| Journal Article | Linear Transformations | Linear Transformations. (2016). Exercises in Linear Algebra, 111-140. doi:10.1142/9789813143050_0004 |
| Book | An Introduction to Linear Transformations in Hilbert Space | Murray, F. (1941). An Introduction to Linear Transformations in Hilbert Space. (AM-4). Princeton University Press. Retrieved from http://www.jstor.org/stable/j.ctt1bc547d |
| Book | Introduction to Linear Algebra | Strang, G. (2016). Introduction to Linear Algebra. Wellesley, MA: Wellesley - Cambridge Press. |
| Book | Linear Algebra and Its Applications | Strang, G. (2006). Linear Algebra and Its Applications. Belmont, CA: Brooks Cole. |
| Book | Matrix Groups for Undergraduates | Tapp, K. (2005). Matrix Groups for Undergraduates. Providence, RI: American Mathematical Society. |
| Title | Description |
|---|---|
| Sine Waves | An applet that allows users to view how view and modify sine waves, modifying both amplitudes and periods. |
| Conic Sections | An applet that allows users to view how each of the conic sections appears as the intersection between a plane and an infinite cone in R^3. |
| Polar Coordinates | An applet that shows users the relationship between rectangular and polar coordinates. |
| Cones and Spheres - Volume | A series of applets that guide users in the derivation of the volume of a cone and sphere in relation to the volume of a cylinder. |
| Upper and Lower Sums | An applet that allows users to visually explore upper and lower sum approximations for a chosen function and number of rectangles. |
| Binomial Distribution | An applet that allows users to visually explore the binomial distribution for chosen values of p and n, and compare the results with a normal distribution. |
| Exploring Matrices and Vectors | An applet that includes a matrix with changeable entries, the standard basis vectors in R^2, and the images of the standard basis vectors when the matrix is applied. |
| Differential Operators as Matrices | An applet that allows a user to input coefficients for a degree 2 polynomial, specify coefficients for a simple linear differential operator, view the matrix form of the differntial operator, view the standard basis vectors in R^3, corresponding to the standard basis for the vector space of polynomials of degree 2, view their images under the differential operator, and view the image of the chosen 2nd degree polynomial under the differential operator. |