Let the matrix A be the idempotent matrix then the Eigen values of the idempotent matrix are _______

According to the property of the Eigen values, the Eigen values of the idempotent matrix are either zero or unity. So, the answer is 0 or 1.

Let the eigen values of a 2 × 2 matrix A be 1, -2 with eigen vectors x₁ and x₂ respectively. Then the eigen values and eigen vectors of the matrix A² - 3A + 4$$I$$ would, respectively, be

2, 14; x1, x2

2, 14; x1 + x2, x1 - x2

2, 0; x1, x2

2, 0; x1 + x2, x1 - x2

For a homogeneous n × n system of linear equations, (A - λ$$I$$)x = 0 having a nontrivial solution, the rank of (A - λ$$I$$) is less than n

For matrix Am, m being a positive integer, (λim, xim) will be the eigen-pair for all i

If AT = A-1, then |λi| = 1 for all i

If AT = A, then λi is real for all i

a, b, c

-a, -b, -c

a-b, b-a, c-a

a-1, b-1, c-1

λ1, λ2, λ3

$ \frac{1}{λ_1}, \frac{1}{λ_2}, \frac{1}{λ_3}$

$λ_1^3, λ_2^3, λ_3^3$

1, 1, 1

-3, -4

-1, -2

-1, -3

-2, -4

zero and +2

-1 and +1

zero and +1

+1 and +1

-2 and -3

2 and 3

4 and 9

16 and 81

1024 and -1024

1024√2 and -1024√2

4√2 and -4√2

512√2 and -512√2