Action of a 2x2 Singular Transformation Matrix in 2D

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This Demonstration shows the action of singular transformation matrices in 2D: all points are either mapped to a line passing through the origin or, if the matrix is null, to the origin itself. Use the sliders to vary three of the elements of the singular matrix.


When the 2D space is mapped to a line, drag the locator to move the point on the left and observe its corresponding image point in the plot on the right.


Contributed by: Roberta Grech (May 2018)
Open content licensed under CC BY-NC-SA



Transformation matrices are studied in pure math courses by high-school students in some countries.

Snapshots 1 and 2: in the case of singular transformation matrices whose entries are not all zero, each point on the image line is the image of infinitely many points—those points on the dashed line in the plot on the left

Snapshot 3: in the case of the singular transformation matrix whose entries are all zero, each point in the plot on the left is mapped to the origin


[1] L. Bostock, S. Chandler and C. Rourke, Further Pure Mathematics, London, UK: Nelson Thornes, 1982.

[2] C. Berry, T. Heard and D. Martin, MEI AS Further Pure Mathematics, 3rd ed., London: Hodder Education, 2004 pp. 33–34.

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