Build custom matrices and transform plotted coordinate sets. Review determinants, traces, and mapped output instantly. Download tables, print reports, and inspect every transformed point.
Sample matrix: [2 1; 0 1] with a unit square.
| Point | Original (x, y) | Transformed (x′, y′) |
|---|---|---|
| P1 | (0, 0) | (0, 0) |
| P2 | (1, 0) | (2, 0) |
| P3 | (1, 1) | (3, 1) |
| P4 | (0, 1) | (1, 1) |
For a 2×2 matrix A and a point vector v, the transformed point is Av.
Matrix: A = [a b; c d]
Point: v = [x; y]
Transformed point: x′ = ax + by
Transformed point: y′ = cx + dy
Determinant: det(A) = ad − bc
Trace: tr(A) = a + d
Area scale factor: |det(A)|
The determinant shows area growth and invertibility. A zero determinant means the transformation collapses the plane into a lower dimension.
This matrix transformation visualizer calculator helps you study how a 2×2 matrix changes points in the Cartesian plane. It turns abstract linear algebra into a direct geometric picture. You can enter any custom matrix, plot several coordinates, and inspect how every point moves after multiplication.
The tool draws the original set and the transformed set on one graph. This makes scaling, shear, reflection, and rotation easier to understand. Dashed geometry shows the starting shape. Solid geometry shows the new shape. This comparison is useful for classroom practice, homework checking, and concept review.
The calculator also reports determinant, trace, area scale, orientation, and invertibility. These values matter in matrix analysis. The determinant tells you if area expands, shrinks, flips, or collapses. The trace gives a quick structural summary. Basis vector output shows where the standard unit directions move under the transformation.
This page is helpful in maths lessons on linear transformations, vector spaces, coordinate geometry, and introductory eigen concepts. Students can test matrix rules with real coordinates. Teachers can generate examples quickly. Tutors can explain why a shape stretches along one direction, skews across an axis, or reflects through a line.
You can export transformed coordinates as CSV for spreadsheet review. You can also save the page as a PDF report for notes or assignments. The mapping table makes each step easy to verify. Because the calculator accepts multiple points, it can model polygons, paths, and simple figures instead of single vectors only.
Use the quick examples to load common transformation types. Then replace them with your own coordinates. Try diagonal matrices for scaling. Try off-diagonal values for shear. Try negative values for reflections. This matrix transformation visualizer calculator gives a fast and structured way to explore linear motion in two dimensions.
It visualizes how a 2×2 matrix transforms a set of 2D points. You can compare the original shape and the transformed shape on one coordinate graph.
The determinant shows area scaling and orientation behavior. A positive value keeps orientation, a negative value flips orientation, and zero means the transformation is not invertible.
Yes. Enter one point per line in the points box. This lets you transform polygons, line segments, sample paths, or any custom coordinate set.
Use either x,y or x y on each line. Examples include 1,2 or 1 2. Parentheses are also accepted and safely ignored.
You can test scaling, reflection, shear, rotation-like matrices, and general linear mappings. Any numeric 2×2 matrix can be entered and applied immediately.
Basis vectors show how the matrix acts on the plane itself. Their transformed positions reveal direction changes, stretch factors, and the structure of the mapping.
A matrix is not invertible when its determinant equals zero. In that case, some geometric information is lost because the plane collapses into a line or point.
Yes. You can download the mapped coordinates as CSV. You can also use the PDF button to save a clean printable copy of the result section.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.