Consider the 2x2 matrix given by: Ho0 - € Ho1 K = (13) H10 H11 - In the above equation H10 = Ho1- 1. Write down the expression for the determinant of K. 2. By setting the determinant of K to zero, determine the two eigenvalues e. 3. Write down an expression for the eigenvector for each of the eigenvalues. Hint: The eigenvalues can be written in the form e4/- = A+/-VB with B a positive number.
Consider the 2x2 matrix given by: Ho0 - € Ho1 K = (13) H10 H11 - In the above equation H10 = Ho1- 1. Write down the expression for the determinant of K. 2. By setting the determinant of K to zero, determine the two eigenvalues e. 3. Write down an expression for the eigenvector for each of the eigenvalues. Hint: The eigenvalues can be written in the form e4/- = A+/-VB with B a positive number.
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Transcribed Image Text:Consider the 2x2 matrix given by:
Ho0 - €
Ho1
K =
(13)
H10
H11 -
In the above equation H10 = Ho1-
1. Write down the expression for the determinant of K.
2. By setting the determinant of K to zero, determine the two eigenvalues e.
3. Write down an expression for the eigenvector for each of the eigenvalues. Hint: The
eigenvalues can be written in the form e+/- = A+/-VB with B a positive number.
4. Write down an expression for the normalized eigenvector of each state.
Complete the equation:
E+/- =
(14)
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