Dot

a.b.c or Dot[a,b,c]

gives products of vectors, matrices, and tensors.

Details

  • a.b gives an explicit result when a and b are lists with appropriate dimensions. It contracts the last index in a with the first index in b.
  • Various applications of Dot:
  • {a1,a2}.{b1,b2}scalar product of vectors
    {a1,a2}.{{m11,m12},{m21,m22}}
    product of a vector and a matrix
    {{m11,m12},{m21,m22}}.{a1,a2}
    product of a matrix and a vector
    {{m11,m12},{m21,m22}}.{{n11,n12},{n21,n22}}
    product of two matrices
  • The result of applying Dot to two tensors and is the tensor . Applying Dot to a rank tensor and a rank tensor gives a rank tensor. »
  • Dot can be used on SparseArray objects, returning a SparseArray object when possible. »
  • When its arguments are not lists or sparse arrays, Dot remains unevaluated. It has the attribute Flat.

Examples

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Basic Examples  (3)

Scalar product of vectors:

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Products of matrices and vectors:

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Matrix product:

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Scope  (2)

Generalizations & Extensions  (1)

Applications  (1)

Properties & Relations  (5)

Possible Issues  (3)

See Also

MatrixPower  Cross  Norm  KroneckerProduct  Inner  Outer  Div  TensorContract  TensorProduct  AffineTransform  NonCommutativeMultiply  VectorAngle  Covariance  LinearLayer  DotLayer

Tutorials

Introduced in 1988
(1.0)
| Updated in 2003
(5.0)