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Eigenvalues and Eigenvectors

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Matrix D: [[3, 1], [0, 3]]

Eigenvalues: 3, 3. Eigenvectors: [1, 0], An infinite number of vectors of the form [1, t] where t is any real number.

Matrix H: [[2, 4], [1, 3]]

Eigenvalues: 1, 4. Eigenvectors: [-2, 1], [2, 1]

Matrix N: [[1,3,0], [-3,1,0], [0,0,2]]

Eigenvalues: 2, 2i, -2i. Eigenvectors: [0, 0, 1], [-3, 1, 0], [3, 1, 0]

Matrix AA: [[3, -2, 4], [-2, 6, 2], [4, 2, 3]]

Eigenvalues: 11, 1, 0. Eigenvectors: [1 1 1], [-2 1 0], [0 -2 1]

Matrix J: [[2, 1, 0], [0, 2, 1], [0, 0, 2]]

Eigenvalues: 2. Eigenvectors: Any vector of the form [a, b, -2a - 2b] where a, b are any real numbers.

Matrix P: [[2, 1, 0], [0, 3, 0], [0, 0, 4]]

Eigenvalues: 2, 3, 4. Eigenvectors: [1, 0, 0], [0, 1, 0], [0, 0, 1]

Matrix Z: [[5, 1], [0, 5]]

Eigenvalues: 5, 5. Eigenvectors: [1, 0], [1, t] where t is any real number

Matrix X: [[3, 0, 2], [0, 3, 0], [2, 0, 0]]

Eigenvalues: 5, 3, -1. Eigenvectors: [1, 0, 1], [0, 1, 0], [-1, 0, 1]

Matrix AC: [[7, 8], [3, 9]]

Eigenvalues: 3, 13. Eigenvectors: [-2, 1], [2, 1]

Matrix V: [[1, 0, 0], [0, 2, 1], [0, 0, 2]]

Eigenvalues: 1, 2. Eigenvectors: [1, 0, 0], [0, 1, -1], [0, 0, 1]

Matrix Q: [[-2, 2, -3], [2, 1, -6], [-1, -2, 0]]

Eigenvalues: 5, 3, -3. Eigenvectors: [1, 1, 1], [3, 2, 0], [1, -1, 1]

Matrix C: [[0, -1], [1, 0]]

Eigenvalues: i, -i. Eigenvectors: [1, i], [1, -i]

Matrix E: [[0, 1], [-2, -3]]

Eigenvalues: -1, -2. Eigenvectors: [1, -1], [1, 2]

Matrix G: [[6, -1], [2, 3]]

Eigenvalues: 5, 4. Eigenvectors: [1, 2], [1, 1]

Matrix AB: [[1, 0, 5], [2, -1, 6], [3, 4, 0]]

Eigenvalues: Approximate numeric solutions required. Eigenvectors: Approximate numeric solutions required.

Matrix B: [[1, 2], [2, 1]]

Eigenvalues: 3, -1. Eigenvectors: [1, 1], [1, -1]

Matrix U: [[1, 4], [2, 3]]

Eigenvalues: 5, -1. Eigenvectors: [2, 1], [-2, 1]

Matrix W: [[1, -1], [1, 1]]

Eigenvalues: 1 + i, 1 - i. Eigenvectors: [i, 1], [-i, 1]

Matrix T: [[2, 1], [1, 2]]

Eigenvalues: 3, 1. Eigenvectors: [1, 1], [1, -1]

Matrix L: [[1,0,0], [0,1,1], [0,0,1]]

Eigenvalues: 1. Eigenvectors: Any vector of the form [t, 0, -t] where t is any real number, and the vector [0, 1, 0].

Matrix A: [[2, 0], [0, 2]]

Eigenvalues: 2, 2. Eigenvectors: [1, 0], [0, 1]

Matrix F: [[4, 1], [0, 4]]

Eigenvalues: 4, 4. Eigenvectors: [1, 0], An infinite number of vectors of the form [1, t] where t is any real number.

Matrix I: [[0, 2], [-2, -3]]

Eigenvalues: -1, -2. Eigenvectors: [2, 1], [-1, 2]

Matrix K: [[4, 0, 1], [0, 4, 0], [1, 0, 4]]

Eigenvalues: 3, 5. Eigenvectors: [-1, 0, 1], [0, 1, 0], [1, 0, 1]

Matrix O: [[1, 0, 1], [0, 2, 0], [-1, 0, 1]]

Eigenvalues: 2, 2, -1. Eigenvectors: [0, 1, 0], [1, 0, 1], [-1, 0, 1]

Matrix S: [[10, 0, 0], [0, 5, 4], [0, -4, 5]]

Eigenvalues: 10, 1, 9. Eigenvectors: [1, 0, 0], [0, 1, -1], [0, 1, 1]

Matrix M: [[7, 0, 0], [0, 2, 0], [0, 0, -1]]

Eigenvalues: 7, 2, -1. Eigenvectors: [1, 0, 0], [0, 1, 0], [0, 0, 1]

Matrix R: [[1, 0, 1], [2, 0, 2], [3, 0, 3]]

Eigenvalues: 0, 0, 4. Eigenvectors: [0, 1, 0], Any vector orthogonal to [1, 0, 1], [1, 0, 1]

Matrix Y: [[0, 2], [-2, 0]]

Eigenvalues: 2i, -2i. Eigenvectors: [1, -i], [1, i]

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