# Week Seven – Tensor Properties: Components & Invariants

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## 11 comments on “Week Seven – Tensor Properties: Components & Invariants”

1. Ororho Maxwell Omorhode says:

Good day sir…sorry to take us back but in the Q&A 2.5 after getting Te1 and substituting v1 =1 ,v2=0,v3= 0.I’m a little confused as to why the coefficients of the result were compared with Te3 and not Te1

• oafak says:

I suspect you have an old copy. There was an error. It has been corrected. Please look at the latest version at the webpage.

2. Temitayo omodehin 160404031 says:

Good day sir, I want to ask why the principal invariants do not change and if it is possible to generate more invariants for a given tensor

• oafak says:

There are other invariants that can formed for a tensor apart from the principal invariants that arise as coefficients of the characteristic polynomial. One such set is as follows: .
These are related to the principal invariants we have been using in this way:

(1)

No matter how you define the invariants, they are related to the characteristic equation of the tensor. These are, in turn, independent of coordinate representation and are functions only of the tensors themselves. That is why they do not vary as you express the tensor in different coordinates. It is the same way a vector’s magnitude and direction are invariants for the vector.
You must not forget though that invariants are only a member of the important scalar-valued functions of the tensor. You can have many many such functions indeed.

• TEMITAYO OMODEHIN 160404031 says:

Thank you very much for the insight, Sir

3. Areo Ajibola says:

Sir, A deviatoric tensor is it necessarily skew? Why?

Areo Ajibola
170407512
Systems Engineering

• oafak says:

In order to be sure you are not simply lazy, you first tell me what you know about a deviatoric tensor and a skew tensor. If after that you still have either of your two questions, I will answer one of them.

• Areo Ajibola says:

Thank you sir. I went back to the textbook and I saw the answer to my question. The deviatoric part of a Tensor depends on the original tensor it is taken.