Matrix normality is one of the most interesting topics in linear algebra and matrix theory, since normal matrices have not only simple structures under unitary similarity but also many applications, that is why it has been done a great deal of work on them. There are $89$ different characteristic properties. In this thesis we chose $25$ of those characteristic properties and proved their equivalence to basic definition of normal matrices. We were also interested in how “close” are the matrices in terms of their eigenvalues. More interestingly, if a matrix is “perturbed” a little bit, how would the eigenvalues of the matrix change? In this thesis we present answers to these two questions if the matrices are normal.
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