Question: Let A be an nxn matrix and let:
B=A + B^T and C=A - A^T
a) Show that B is symmetric and C is skewed symmetric.
b) Show that every nxn matrix can be represented as a sum of a symmetric matrix and a skew symmetric matrix.
I'm not certain how to tackle this. Firstly, the book I am using does not define the term 'skewed symmetry'. What does it mean? Any helps/tips/prompts etc most welcome.
On a more general note, I've just started linear algebra and can see myself getting quite overwhelmed as I lack the intuitive ability to work well with matrices. Can any of you fine gentlemen give me any tips for keeping afloat?
Many thanks for your consideration.