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MATH / LINEAR ALGEBRA

2x2 Matrix Eigenvalue Calculator

Calculate both real eigenvalues of a two-by-two matrix. Review the equation, substituted values, result, assumptions, and interpretation in one focused workspace.

  • 01 Calculated in this tab
  • 02 Values stay in this browser tab
  • 03 Use boundary

Conversion input

Known value

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Use boundary

Calculation path

Calculate both real eigenvalues of a two-by-two matrix. The page evaluates the displayed equation from your supplied values and presents both symbolic and substituted KaTeX working so the arithmetic can be checked.

Calculation path

lambda=(a+d +/- sqrt((a-d)^2+4bc))/2

What you provide

What you provide

  • Top-left entry, using the same scenario as the other inputs
  • Top-right entry, using the same scenario as the other inputs
  • Bottom-left entry, using the same scenario as the other inputs
  • Bottom-right entry, using the same scenario as the other inputs

What you receive

What you receive

  • Larger eigenvalue from the stated equation
  • A symbolic formula plus substituted working with your values
  • Visible assumptions, field guidance, and an authoritative learning reference

Use boundary

Choose the maximum decimal places shown. This does not increase source accuracy.

This page reports real eigenvalues only.

Use internally consistent units and retain extra precision when carrying the result into another calculation.

Reviewed reference factors

Reviewed reference factors