Calculator
Example Data Table
| Case | Input | Rule Applied | Infinity Norm |
|---|---|---|---|
| Vector Example | [-3, 7, -2, 5] | Largest absolute entry | 7 |
| Matrix Example |
[1, -2, 3] [4, -1, 2] [-3, 5, -6] |
Largest absolute row sum | 14 |
| Vector Example | [0.5, -8.2, 4.1] | Largest absolute entry | 8.2 |
Formula Used
For a Vector
‖x‖∞ = max |xi|
Take the absolute value of each vector entry. The infinity norm equals the largest absolute value among all components.
For a Matrix
‖A‖∞ = max ∑ |aij|
Compute the sum of absolute values across each row. The infinity norm equals the largest of those row sums.
How to Use This Calculator
- Choose whether you want to evaluate a vector or a matrix.
- Enter your values in the correct input area.
- For vectors, choose comma, space, or automatic delimiter detection.
- Select the number of decimal places for displayed results.
- Press Calculate Infinity Norm to generate the answer.
- Review the result card, breakdown table, steps, and graph.
- Use the export buttons to save the calculation as CSV or PDF.
FAQs
1. What is an infinity norm?
The infinity norm measures the largest magnitude used in a vector or matrix. For vectors, it is the maximum absolute entry. For matrices, it is the maximum absolute row sum.
2. How does the vector infinity norm work?
The calculator converts each vector value to its absolute value and then finds the largest one. Negative signs do not affect the final comparison because absolute values are used.
3. How does the matrix infinity norm work?
The calculator computes the sum of absolute values within each row. It then compares those row totals and returns the largest row sum as the matrix infinity norm.
4. Can I enter decimals and negative numbers?
Yes. The calculator accepts integers, decimals, and negative values. It automatically uses absolute values where needed during the infinity norm computation.
5. Why must matrix rows have equal length?
A valid matrix requires every row to contain the same number of entries. Unequal row lengths would create inconsistent dimensions and invalidate the matrix norm calculation.
6. What does the graph show?
The graph displays the values compared in the norm calculation. For vectors, it shows absolute component magnitudes. For matrices, it shows absolute row sums.
7. When is the infinity norm useful?
It is useful in numerical analysis, optimization, error bounds, matrix conditioning, and stability studies. It helps identify the largest dominating component or row contribution.
8. What is the difference between vector and matrix infinity norms?
The vector infinity norm uses the maximum absolute entry. The matrix infinity norm uses the maximum absolute row sum. Both focus on the largest dominating magnitude.