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Animated Matrix -Vector Multiplication

The animation illustrates the multiplication a \(5 \times 5\) matrix by a \(5 \times 1\) vector, \(A\mathbf{x}\), computed as linear combinations of the columns of \(A\). The weights in the linear combination are the components of \(\mathbf{x}\). The scalar multiples of the columns are computed, then the sum of the resulting vectors is displayed. After the animation completes, clicking Start gives a different matrix and vector.

Average: 3.5 (11 votes)
C. J. Kentler and Alan Genz
Judi McDonald / David Hill
Washington State University website
C. J. Kentler and Alan Genz
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Anonymous's picture

This is a really nice program that illustrates how we think about matrix multiplication's picture

Has some glitches. Pressing start causes speed to return to default (too fast). Often the vector is missing an entry and/or its right bracket.

yasskin's picture

Beautiful animations. It's really nice that there is a restart button which modifies the matrix and the vector.

Anonymous's picture

Cute animation showing how to multiply a matrix times a vector by taking a linear combination of the columns of the matrix.