Element-wise Absolute Value Calculator
Apply the absolute value to every element of a matrix. Negative entries become positive; positive entries remain unchanged.
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Notes
Element-wise Absolute Value
The element-wise absolute value replaces every entry with its magnitude (distance from zero). Negative entries become positive; non-negative entries are unchanged.
Example
Input A:
| -3 | 2 |
| 0 | -7 |
Element-wise |A|:
| 3 | 2 |
| 0 | 7 |
This is not the matrix absolute value (which is defined via eigenvalue decomposition). This calculator applies |·| to each entry independently.
See also
- Matrix Calculations Guide — Element-wise Operations — In-depth notes on Element-wise Operations with worked examples
Frequently Asked Questions
Does this change the matrix rank?
Not necessarily, but it can. For example, a row [1, −1] has absolute value [1, 1], which may change the linear independence of rows.
Is element-wise |A| the same as the matrix absolute value?
No. The matrix absolute value is defined as A = √(A^T A) via SVD, which is much more complex.
What is a practical use of element-wise absolute value?
Computing the 1-norm or ∞-norm of a matrix requires summing absolute values of entries. It is also used in robust statistics and signal processing.