Calculates the coefficients of a characteristic equation (cubic). (Fractions, complex numbers)
Author: shiroeExecutions: 71
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Enter the elements of a 3-row by 3-column matrix (determinant) as fractions.
Enter aij as the numerator and bij as the denominator. (i is the row; j is the column; i, j = 1, 2, 3)
Output the results as fractions, except for the coefficient of the highest degree, which is -1.
Enter aij as the numerator and bij as the denominator. (i is the row; j is the column; i, j = 1, 2, 3)
Output the results as fractions, except for the coefficient of the highest degree, which is -1.
| λ³ term coefficient | Coefficient of the highest-order term (=-1) |
| The numerator of the λ² term coefficient | |
| The denominator of the λ² term coefficient | |
| The numerator of the λ^1 term coefficient | |
| The denominator of the λ^1 term coefficient | |
| Constant term in the numerator | |
| Constant term in the denominator | |
| Values of the λ² term coefficients (numerator/denominator) | (Decimal format) |
| Value of the λ^1 term coefficient (numerator/denominator) | (Decimal format) |
| Value of the constant term (numerator/denominator) | (Decimal format) |
Digit display setting: 50 digits.
Digit count can be changed.
Complex number calculation mode.
R6 (2024).05/24 (Fri)_Ver.001
Routine, n=3,,
koishi,,K,001
Digit count can be changed.
Complex number calculation mode.
R6 (2024).05/24 (Fri)_Ver.001
Routine, n=3,,
koishi,,K,001
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Since we are considering the eigenvalue problem for a 3x3 square matrix,
the characteristic equation is derived from the determinant of a 3-row by 3-column matrix.
The form of the cubic characteristic equation is
-(λ³) + m*(λ²) + n*(λ¹) + a constant term.
The coefficient of the term of the highest degree (λ³) remains -1.
Calculate and output the coefficients of the (λ²) term, the (λ¹) term, and the constant term.
The form of the characteristic equation is displayed in its expanded form.