This lesson covers the concept of principal stresses and their direction cosines in the field of mechanics. It explains how to determine the principal stresses using the characteristic equation and how to find the corresponding direction cosines. The lesson also illustrates these concepts with an example involving a stress tensor. It further discusses the proof that principal directions are mutually orthogonal and that principal stresses are real. The lesson concludes with a set of problems for self-practice, encouraging learners to apply the concepts learned.

- Principal stresses can be determined using the characteristic equation.
- The direction cosines corresponding to a particular stress can be found by solving a set of equations.
- Principal directions are mutually orthogonal, which can be proven using tensor notation.
- Principal stresses are real, not complex, which can be demonstrated through the roots of the characteristic equation.

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