Calculates the coefficients and solutions of the characteristic equation of a 2x2 square matrix.
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Let the elements of a 2x2 square matrix be m11, m12, m21, and m22. Enter these values.
m11 is the element in the first row and first column.
m12 is the element in the first row and second column.
m21 is the element in the second row and first column.
m22 is the element in the second row and second column.
Replace the diagonal elements m11 and m22 with (m11 - λ) and (m22 - λ), respectively, expand the expression, and
rewrite it in the familiar quadratic equation form: Aλ² + Bλ + C = 0.
When the eigenvalue is the solution (1) = α, calculate m11 - α and m22 - α for the diagonal elements and display the matrix elements.
When the eigenvalue is the solution (2) = β, calculate m11 - β and m22 - β for the diagonal elements and display the matrix elements.
m11 is the element in the first row and first column.
m12 is the element in the first row and second column.
m21 is the element in the second row and first column.
m22 is the element in the second row and second column.
Replace the diagonal elements m11 and m22 with (m11 - λ) and (m22 - λ), respectively, expand the expression, and
rewrite it in the familiar quadratic equation form: Aλ² + Bλ + C = 0.
When the eigenvalue is the solution (1) = α, calculate m11 - α and m22 - α for the diagonal elements and display the matrix elements.
When the eigenvalue is the solution (2) = β, calculate m11 - β and m22 - β for the diagonal elements and display the matrix elements.
| m11 | m12 Reposted for clarity |
| m21 | m22 Reposted for clarity |
| Coefficient A | Coefficient B Coefficient C |
| Discriminant | Value of the discriminant D |
| Square Root of the Discriminant (1) | +√D |
| Square Root of the Discriminant (2) | -√D |
| Solution (1) | |
| Solution (2) | |
| Value of the determinant | Values of the determinants of the matrices with elements m11, m12, m21, and m22 |
| Element 11 | When λ = Solution (1)Element 12 When λ = Solution (1) |
| Element 21 | When λ = Solution (1)Element 22 When λ = Solution (1) |
| Element 11 | When λ = Solution (2)Element 12 When λ = Solution (2) |
| Element 21 | When λ = Solution (2)Element 22 When λ = Solution (2) |
R6 (2024). August 12 (Mon)_Ver. 001
50-digit setting. Digit count can be changed. Complex number calculation mode.
50-digit setting. Digit count can be changed. Complex number calculation mode.
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Displays the coefficients of the characteristic equation.
Although the characteristic equation is a quadratic equation, it calculates the value of the discriminant D.
It also displays the square root of the discriminant.
It outputs the solutions to the characteristic equation.
If there are repeated roots, it displays two solutions. If the discriminant is 0, there are repeated roots.