Calculating Cubic Expressions for a 2x2 Square Matrix
Author: shiroeExecutions: 28
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Enter the elements of x, aL, aR, bL, bR, cL, cR, and d.
By default, aL, aR, bL, bR, cL, and cR are identity matrices.
The numbers to the right of the letters in the input fields represent the row and column indices of the matrix.
Please do not leave any fields blank.
The output of the determinant of y is provided for reference only.
By default, aL, aR, bL, bR, cL, and cR are identity matrices.
The numbers to the right of the letters in the input fields represent the row and column indices of the matrix.
Please do not leave any fields blank.
The output of the determinant of y is provided for reference only.
| y11 | y12 |
| y21 | y22 |
| Value of the determinant of y |
R6 (2024). Nov. 6 (Wed). Ver_003.
Digit display setting: 50 digits. Digit count can be changed. Complex number calculation mode.
Digit display setting: 50 digits. Digit count can be changed. Complex number calculation mode.
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Let y, x, aL, aR, bL, bR, cL, cR, and d be a 2x2 square matrix.
The form of the expression is
y = aL * x * x * x * aR + bL * x * x * bR + cL * x * cR + d
.
This mimics the cubic equation y = ax³ + bx² + cx + d for “ordinary numbers” with respect to x.
L and R denote the left and right positions relative to the exponent of x, respectively.
* denotes matrix multiplication, where the right matrix is multiplied by the left matrix.
Multiple * operations are performed sequentially, multiplying the right matrix by the left matrix each time.
Finally, the terms are added together.