Are vectors coordinate independent?

Vectors are independent of the coordinate system. They depend of the frame, though, and Galilean transform changes the frame of reference. However forces are independent of the frame of reference!

Are tensors coordinate independent?

In other words, the tensor A is a linear combination of such “direct products”. The most important observation is that the Eq. (1.18) transforms as a scalar. Hence, despite the components of a tensor are dependent on the choice of the basis, the tensor itself is coordinate-independent.”

What is the difference between a vector and a tensor?

Any quantity that has both magnitude and direction is called a vector. Velocity, acceleration, and force are some example. But tensor is a quantity which needs direction,magnitude and plane to define.

Is position vector a tensor?

i.e., while the position vector itself is not a tensor, the difference between any two position vectors is a tensor of rank 1! V1 and V1* both represent the same point, but their coordinate is different due to different basis. It looks like the difference between two position vectors is NOT the same.

What does coordinate independent mean?

It has also been alleged that coordinate independence is trivial. Coordinate independence tells us that when we solve problems, we should avoid writing down any equations in notation that isn’t manifestly intrinsic, and avoid interpreting those equations as if the coordinates had intrinsic meaning.

Which of the following is independent of coordinate system?

The answer will be (A) that is P vector + Q vector + R vector.

How is a tensor different from a matrix?

In a defined system, a matrix is just a container for entries and it doesn’t change if any change occurs in the system, whereas a tensor is an entity in the system that interacts with other entities in a system and changes its values when other values change.

Is every vector a tensor?

All vectors are, technically, tensors. All tensors are not vectors. This is to say, tensors are a more general object that a vector (strictly speaking though, mathematicians construct tensors through vectors).

What is not a tensor?

The notions of vector and scalar from freshman mechanics are distinguished from one another by the fact that one has a direction in space and the other does not. Therefore we expect that area would be a scalar, i.e., a rank-0 tensor. We therefore conclude that quantities like area and volume are not tensors.

Why is position a vector not a tensor?

This is why the absolute position vector pointing from the origin to a particular object in space is not a tensor, because the components of its representation depend on the absolute values of the coordinates. In contrast, the coordinate differentials transform based solely on local information.

Why do we need independent coordinates?

Coordinate independence tells us that when we solve problems, we should avoid writing down any equations in notation that isn’t manifestly intrinsic, and avoid interpreting those equations as if the coordinates had intrinsic meaning.

What are vectors and tensor?

VECTOR AND TENSOR ANALYSIS In basic engineering courses, the term vector is used often to imply a physical vector that has “magnitude and direction and satisfies the parallelogram law of addition.” In mathematics, vectors are more abstract objects than physical vectors. Like physical vectors, tensors

What is a second order tensor?

SECOND-ORDER TENSORS . A second-order tensor is one that has two basis vectors standing next to each other, and they satisfy the same rules as those of a vector (hence, mathematically, tensors are also called vectors). A second-order tensor and its . transpose. can be expressed in terms of rectangular Cartesian base vectors as

What is a vector in mechanics?

A vector is a directed line segment and provides one of the most useful geomet­ ric constructs in mechanics. A vector can be used for a variety of purposes. For example, in Fig. 2 the vector v records the position of point b relative to point a.