Online graphically matrix vector product

Multiplication of a Vector v with a Matrix M: w = M ⋅ v

w=Mv= ( m11m12 m21m22 ) ( vx vy )

The operation with the vector is graphically presented. By moving the vector endpoint the vector can be changed. The sliders change the matrix elements. The red vector is the result vector of the multiplication with the matrix.

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m11 =
m12 =
vx =
m21 =
m22 =
vy =

Axes ranges

x-min=
x-max=
y-min=
y-max=

Slider ranges

m11-min=
m12-min=
m21-min=
m22-min=
m11-max=
m12-max=
m21-max=
m22-max=

Multiplication of a vector with a matrix

The product of a matrix with a vector is a linear image. The multiplication is explained if the number of columns of the matrix is equal to the number of elements of the vector. The result is a vector whose number of components equals the number of rows of the matrix. This means that a matrix with 2 rows always maps a vector to a vector with two components.

Av= ( a11a12a1m a21a22a2m an1an2anm ) ( v1 v2 vm ) = ( a11v1+a12v2++a1mvm a21v1+a22v2++a2mvm an1v1+an2v2++anmvm )

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