Math 210-01: Linear Algebra: Reading Homework 8.5

1. Unitary and Hermitian Matrices : what types of matrices do unitary and Hermitian matrices correspond to?
   
   1. Conjugate Transpose : what is the conjugate transpose?
      
      1. properties : how is the conjugate transpose written? what properties does it have?
         
   2. Unitary matrices : what is a unitary matrix? how is this similar to orthogonal matrices?
      
      1. properties of unitary matrices : what can we say about the columns of a unitary matrix? how is this similar to orthogonal matrices?
         
   3. Hermitian matrices : what is a Hermitian matrix? how is this similar to symmetric matrices?
      
      1. properties : what characteristics must a Hermitian matrix have?
         
      2. eigenvalues : what is true about the eigenvalues of a Hermitian matrix?
         
      3. eigensystems : how do we find the eigenvalues and eigenvectors of a comples matrix?
         
   4. Diagonalization : what is the complex-valued equivalent to orthogonal diagonalization for real-valued matrices? what types of matrices fall in this category?
      
      1. normalization : how do we normalize the column vectors in a complex matrix?
         
      2. normal matrices : are there other matrices that are unitarily diagonalizable?
         
   5. Hermitian and Symmetric Matrices : summarize the properties of symmetric and Hermitian matrices, their similarities and differences