"1. When you has the repeated eigenvalue (eg. repeated 2 times as multiplicity, 2), does it matter to the solution?

2. Is it okay if I forget to write underline for matrix or vector in the exam?"

1. It depends on what you are trying to calculate.

- For just calculating eigenvectors you can use the multiplicity as a check. The eigenspace dimension should be less than or equal to the multiplicity of that eigenvalue. The eigenspace is just the number of linearly independent eigenvectors you get after row reduction.

- For orthogonal diagonalisation (not examined) we have that a symmetric matrix will have have an eigenspace with dimension exactly equal to the multiplicity of that eigenvalue. This will affect the process to orthogonally diagonalise a matrix (see lecture notes 7 page 12).

- Finding Jordan normal form (not examined) the multiplicity of the eigenvalue tells you how many linearly independent generalised eigenvectors you will find.

2. I will not subtract marks but it is important for clarity so that I know whether your are talking about vectors, matrices or scalar quantities. Remember, you must make your mathematical argument clear to me so I can grade your understanding. If it is not clear to me that you know what you are talking about then I will not be awarding marks.