CALCULATOR
2×2 Characteristic Polynomial at Lambda Calculator
2×2 Characteristic Polynomial at Lambda Calculator — change the supplied values to calculate 2×2 characteristic polynomial at lambda.
Real numeric 2×2 matrix only; this evaluates the polynomial at one supplied lambda, without finding roots or symbolic factors.
Accepted inputs: A: -100 to 100 number; B: -100 to 100 number; C: -100 to 100 number; D: -100 to 100 number; Lambda: -100 to 100 number.
How the calculation works
p(λ)=(λ-a)(λ-d)-bc
Expand det(λI−A), equivalently λ²−trace(A)λ+det(A).
Worked example
With a 2 number, b 1 number, c 3 number, d 4 number, lambda 1 number, 2×2 characteristic polynomial at lambda is 0 number.
Assumptions and limits
Real numeric 2×2 matrix only; this evaluates the polynomial at one supplied lambda, without finding roots or symbolic factors.