This graph allows you to visualize 2D linear transformations, in a way that can hopefully give you a good intuition for some linear algebra concepts.

Apr 28, 2021 · Here's a basic idea. A matrix takes the xy-plane and alters it in some way, whether that be stretching, shrinking, rotating, etc. Take the first column of the matrix. That vector is the result when you move the vector $\begin{pmatrix} 1 \\ 0 \end{pmatrix}$ to that first column vector.

Oct 11, 2021 · Change the entries of the matrix and hit enter to update the transformed image of Lena. \[ \mathbf M=\begin{pmatrix} \FormInput[2][matrix-entry][1]{a} & \FormInput[2][matrix-entry][0]{b}\\ \FormInput[2][matrix-entry][0]{c} & \FormInput[2][matrix-entry][1]{d} \end{pmatrix} \]

Play around with different values in the matrix to see how the linear transformation it represents affects the image. Notice how the sign of the determinant (positive or negative) reflects the orientation of the image (whether it appears "mirrored" or not).

Linear Transformation Visualizer - Inspired by 3Blue1Brown. t: (0) Show In/Out Vector. Show Determinant. Show Eigenvectors. Snap to Grid. Instructions. Drag the green and red targets to set in the transformed basis vectors. Drag the t slider to visualize the transformation.

A 2 × 2 matrix can be used to apply a linear transformation to points on a Cartesian grid. A linear transformation in two dimensions has the following properties: The origin (0,0) is mapped to the origin (it is invariant) under the transformation; Straight lines are mapped to straight lines under the transformation

In this interactive, you will be able to play around with and visualize how various 2x2 matrices transform points in space. The primary function of a matrix is as something that can be multiplied by a vector to get another vector. As such, we can think about matrices as functions that take vectors as inputs and output vectors.

What stays the same, what is different when the sliders are changed? What effect does the determinant have on the area? What happens if the determinant is 0? What does it mean if there is a negative determinant?

This is a visualizer for matrix transformations on a 2D graph. Use z to apply your matrix, x to change indices, and the up/down arrow keys to adjust the value for that index. This is inspired by 3blue1brown's linear algebra videos .

Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.