Block Diagonal Eigenvalues

Problem

Compute the eigenvalues of a block diagonal matrix given as a list of diagonal blocks.

Each block is either 1x1 (its scalar) or 2x2, solved from lambda^2 - tr*lambda + det = 0. Return all eigenvalues sorted ascending, or None if any 2x2 block has complex eigenvalues (negative discriminant).

Hint

Eigenvalues of a block diagonal matrix are the union of the blocks' eigenvalues.

Test cases

case 1

in: [[[[2,0],[0,3]],[[4]]]]

expected: [2,3,4]

case 2

in: [[[[1,1],[0,2]]]]

expected: [1,2]

case 3

in: [[[[0,-1],[1,0]]]]

expected: null

case 4

in: [[[[5]]]]

expected: [5]

case 5

in: [[[[3,0],[0,3]],[[-1]]]]

expected: [-1,3,3]

Starter codePython

def block_diagonal_eigenvalues(blocks):
    # Your code here
    pass

5 test cases · run your code against them in the editor