I am doing vector analysis. I have figured out that the following expression won't be simplified in Mathematica

Simplify[Dot[x, y] - Dot[y, x]]

I think the reason is that x and y could be matrix, so generally the operation does not commute. But for a vector, the commutation relation should hold. What I don't know is how to tell Mathematica to consider x and y to be vectors.

Also, how can I expand Cross[x + y, z] to be Cross[x, y] + Cross[y, z]? I tried to use Expand and ExpandAll but neither worked.

BTW, in Mathematica, is it possible to define a abstract row/column vector without explicitly specify the number of entries?

I am doing vector analysis. I have figured out that the following expression won't be simplified in Mathematica:

Simplify[Dot[x, y] - Dot[y, x]]

I think the reason is that x and y could be matrices, so generally the operation does not commute. But for a vector, the commutation relation should hold. What I don't know is how to tell Mathematica to consider x and y to be vectors.

Also, how can I expand Cross[x + y, z] to be Cross[x, y] + Cross[y, z]? I tried to use Expand and ExpandAll but neither worked.

BTW, in Mathematica, is it possible to define a abstract row/column vector without explicitly specifying the number of entries?

I am working on vector analysis and figure out that the following expression won't be simplified in Mathematica

Simplify[Dot[x, y]-Dot[y,x]]

I think the reason is that x and y could be matrix so in general, the operation does not commute. But for vector, the commutation relation should hold but how can I force the interpreter to consider x and y to be vector not matrix?

Also, how do we expand Cross[x+y, z] to be Cross[x, y] + Cross[y, z]? I try to use Expand and ExpandAll but didn't work.

BTW, in Mathematica, is that possible to define a abstract row/column vector without explicitly specify the number of entries?

I am doing vector analysis. I have figured out that the following expression won't be simplified in Mathematica

Simplify[Dot[x, y] - Dot[y, x]]

I think the reason is that x and y could be matrix, so generally the operation does not commute. But for a vector, the commutation relation should hold. What I don't know is how to tell Mathematica to consider x and y to be vectors.

Also, how can I expand Cross[x + y, z] to be Cross[x, y] + Cross[y, z]? I tried to use Expand and ExpandAll but neither worked.

BTW, in Mathematica, is it possible to define a abstract row/column vector without explicitly specify the number of entries?

I am working on vector analysis and figure out that the following expression won't be simplified in Mathematica

Simplify[Dot[x, y]-Dot[y,x]]

I think the reason is that x and y could be matrix so in general, the operation does not commute. But for vector, the commutation relation should hold but how can I force the interpreter to consider x and y to be vector not matrix?

Also, how do we expand Cross[x+y, z] to be Cross[x, y] + Cross[y, z]? I try to use Expand and ExpandAll but didn't work.

I am working on vector analysis and figure out that the following expression won't be simplified in Mathematica

Simplify[Dot[x, y]-Dot[y,x]]

I think the reason is that x and y could be matrix so in general, the operation does not commute. But for vector, the commutation relation should hold but how can I force the interpreter to consider x and y to be vector not matrix?

Also, how do we expand Cross[x+y, z] to be Cross[x, y] + Cross[y, z]? I try to use Expand and ExpandAll but didn't work.

BTW, in Mathematica, is that possible to define a abstract row/column vector without explicitly specify the number of entries?