Matrix Calculator
Matrix is evaluated from Operation, Matrix A - Row 1, Col 1 and Matrix A - Row 1, Col 2. The calculation reports Result [1,1], Result [1,2] and Result [2,1].
Results
About the Matrix Calculator
The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.
Formula basis:
Add: element-wise sum
Multiply: C[i][j] = row i of A · column j of B
det(A) = ad - bc
Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.
Formula & How It Works
The calculation applies the following relations exactly as recorded in the metadata: Add: element-wise sum Multiply: C[i][j] = row i of A · column j of B det(A) = ad - bc Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.
Worked Examples
Example 1: 2D Rotation Matrix — 90°
Inputs
With Operation = A x B (Multiply), Matrix A - Row 1, Col 1 = 0, Matrix A - Row 1, Col 2 = -1 and Matrix A - Row 2, Col 1 = 1 as the stated inputs, the result is Result [1,1] = -4, Result [1,2] = 0 and Result [2,1] = 3. Each value corresponds to the declared output fields.
Example 2: Network Analysis — Adjacency Matrix Squared
Inputs
With Operation = A x B (Multiply), Matrix A - Row 1, Col 1 = 0, Matrix A - Row 1, Col 2 = 1 and Matrix A - Row 2, Col 1 = 1 as the stated inputs, the result is Result [1,1] = 1, Result [1,2] = 0 and Result [2,1] = 0. Each value corresponds to the declared output fields.
Example 3: Economics — Input-Output Leontief Model
Inputs
With Operation = A + B (Add), Matrix A - Row 1, Col 1 = 0.3, Matrix A - Row 1, Col 2 = 0.2 and Matrix A - Row 2, Col 1 = 0.1 as the stated inputs, the result is Result [1,1] = 1.3, Result [1,2] = 0.2 and Result [2,1] = 0.1. Each value corresponds to the declared output fields.
Example 4: Scalar Multiplication — Scale Up Data
Inputs
With Operation = k x A (Scalar), Matrix A - Row 1, Col 1 = 3, Matrix A - Row 1, Col 2 = 1 and Matrix A - Row 2, Col 1 = 4 as the stated inputs, the result is Result [1,1] = 7.5, Result [1,2] = 2.5 and Result [2,1] = 10. Each value corresponds to the declared output fields.
Common Use Cases
- Multiply transformation matrices in graphics
- Solve simultaneous equations using matrices
- Apply linear transformations in machine learning
- Calculate covariance matrices in statistics