OK, tensorship is not a word, but if you are an array that holds together a bunch of numbers, and you aspire be certified as a tensor, the will make you prove you are invariant to
Your invariant character is why physicists will love you–after they stop hating you.
Below is a small story that lets you show your stuff. A vector is a magnitude and a direction and it is convenient. to express it in polar coordinates, The variable ‘r’ is the magnitude and the angle 
Cartesian Space boasts of how easily the addition of vectors can be–“just add equivalent components!” (This is sometimes referred to as component-wise addition.)
1. Convert the old vectors from Polar to Cartesian.
2. Do the vector addition calculations to convert old vectors to new vectors.
3. Convert the new vectors from Cartesian to Polar.
Appendix A
One way to understand what a tensor is is to find a pseudotensor ask him, why did you fail when you applied for tensor certification?
Sign change is one sin committed by a pseudotensor. Pseudovectors also commit this sin.
The story gets more weird as we put our forensic Minds to it. Re-read that they’re doing improper rotation as the inverse to rotation. That is not correct. The inverse to a 30 degree rotation is a -30 degree rotation not a 30 degree improper Rotation. By definition improper rotation does rotation and then does a reflection which is how you get that negative sign.
The error comes from making an incorrect choice for the inverse operation – – well, what if it was intentional…
Maybe, we have a story where we need this behavior. If this is true then a real tensor is bad and the pseudotensor is good. Suddenly the bad boy Bruno is the hero.
Vectoreverything 