Element-wise Square Root Calculator
Apply the square root function to every element of a matrix. All entries must be ≥ 0.
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Notes
Element-wise Square Root
The element-wise square root applies √ to each entry independently. This is distinct from the matrix square root (X such that X² = A).
Example
Input A (all entries non-negative):
| 4 | 9 |
| 16 | 25 |
Element-wise √A:
| 2 | 3 |
| 4 | 5 |
All elements must be non-negative (≥ 0). Negative entries cause a domain error.
See also
- Matrix Calculations Guide — Element-wise Operations — In-depth notes on Element-wise Operations with worked examples
Frequently Asked Questions
Is this the same as the matrix square root?
No. The matrix square root finds X such that X·X = A. Element-wise square root applies √ independently to each entry.
What if a cell contains a negative number?
The square root is undefined for real negative numbers. This calculator will show an error for any negative entry.
Is element-wise √ the same as element-wise power 0.5?
Yes. √x = x^(1/2), so element-wise sqrt is identical to element-wise power with exponent 0.5.