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Matrix-Vector Multiplication


The product of an m×n matrix A=(a_(ij)) and a column vector x=(x_1,...,x_n)^T is the vector y=Ax in which

 y_i=sum_(j=1)^na_(ij)x_j for i=1,...,m.

Equivalently, Ax is a linear combination of the column vectors of A with coefficients supplied by x. Matrix-vector multiplication is the coordinate form of applying a linear transformation.


See also

Linear Transformation, Matrix Multiplication, Vector

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References

Axler, S. Linear Algebra Done Right, 2nd ed. New York: Springer-Verlag, 1997.

Cite this as:

Weisstein, Eric W. "Matrix-Vector Multiplication." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Matrix-VectorMultiplication.html

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