What is a tensor and how does it differ from a vector?

[yaswanth_040]

Hi all,
What is a tensor? Can any give a practical use of it? How it is different from Vector?

Thank You,
Yaswanth

 

[viscousflow]

Tensor is a vector generalized to 3Dimensions. Tensors are typically found in structural engineering for instance with anisotropic materials with characteristics which change in direction. Here you can see a typical strain tensor

http://en.wikipedia.org/wiki/Deformation_(mechanics)#Shear_strain

Other topics include inertia, and strength.

 

[Mech_Engineer]

A tensor is basically decribed in the analogy:

Scalar : Vector :: Matrix : Tensor

http://en.wikipedia.org/wiki/Tensor

 

[RandomGuy88]

Try thinking of a vector but with two dimensions that is written down in matrix form. For example the strain tensor in a solid like Viscousflow mentioned. Or the stress tensor in a fluid. The the components of the stress tensor are

Txx Txy Txz
Tyx Tyy Tyz
Tzx Tzy Tzz

So for an element in the fluid Txx would be the stress on the x face in the x direction. So it is a normal stress or pressure. Txy would be the stress on the x face in the y direction, shear stress caused by viscosity.