Unitary Similarity Diagonalization of a Square Hermitian Matrix

UNITARY SIMILARITY DIAGONALIZATION OF A SQUARE HERMITIAN MATRIX [12] 

Let [A] be an n X n matrix (and Hermitian symmetric for quantum mechanics) with eigenvectors 

From this demonstration, you can see that we need to find a way to divide matrices as in [T] [T] = [T] Ht] = [T [7( . Well, there is no such thing as matrix division although there is a way to get an inverse as T. A student should know/leam that there is a tedious way to find the inverse of 

Fortunately there is a short cut we can use most of the time when [T] is unitary (formed from 

We are taking a lot of space here to illustrate the very important technique of diagonalizing a matrix with a simple (2 x 2) example but there should be no doubt that this is one of the essentials of modern physical chemistry. Modem quantum chemistry programs use this concept hundreds of times in every calculation, often for matrices of dimension (100 x 100) or more Well then let us 

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