A tensor is a mathematical quantity that describes the relationship between different vectors or sets of vectors, while a vector is a mathematical object that represents a quantity with both magnitude and direction.
Yes, a vector can be seen as a special case of a tensor where the order (or number of indices) is equal to 1.
Vectors transform in a specific way under coordinate transformations, while tensors transform according to specific rules depending on their order or rank.
Tensors are commonly used in physics and engineering to describe the properties of physical systems, while vectors are often used in mathematics and physics to describe quantities such as velocity, acceleration, or force.
Tensors of the same order and dimensions can be added together, while tensors and vectors of different orders cannot be added or multiplied together in a meaningful way.