Week Nine – Tensor Properties III: The Eigenvalue Problem

In this last week of lectures before your second test, we shall be looking at the Eigenvalue problem you have encountered already in your Engineering Mathematics. There is an equipollency between the tensor eigenvalues and those of matrices. The issues here are therefore familiar. The tensor form has specific physical implications in our engineering courses especially as it relates to the Principal invariants of tensors and the spectral form using eigenbases.
We shall also have two tutorial classes on the worked examples to help prepare you for the test. Remember that the test is a paraphrase of the same problems that are solved for you in the Q&A at the end of each chapter. EVERYTHING in the Q&A is part of the questions populating the database from where your questions are drawn.

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Week Eight – Tensor Properties II: Decompositions & Orthogonal Tensors

This week we continue our study of tensor properties with additive and spectral decompositions of tensors. We shall also look at orthogonal tensors. The slides are presented in the video

Here are the actual slides we will use in class. It begins with a repeat of some of last week’s outstanding issues that you ought to have gone through on your own. These are: Products of determinants, trace of compositions and scalar product of tensors. You must be current on these in order to understand this weeks menu.
The five topics covered here include:
1. The tensor set as a Euclidean Vector Space,
2. Additive Decompositions
3. The Cofactor Tensor, its geometric interpretation
4. Orthogonal Tensors
5. The Axial Vector
These are vocalized in the above Vimeo video and the downloadable slides are here

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