Element-wise Exponential Calculator
Apply the exponential function e^x to every element of a matrix. Works for any real entries.
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Notes
Element-wise Exponential
The element-wise exponential applies e^x to each matrix entry independently. All entries of the result are always positive.
Example
Input A:
| 0 | 1 |
| 2 | -1 |
Element-wise exp(A): e^0=1, e^1≈2.718, e^2≈7.389, e^(−1)≈0.368
| 1 | 2.718 |
| 7.389 | 0.368 |
This is the Hadamard exponential. The matrix exponential e^A (used in differential equations) is much more complex.
See also
- Matrix Calculations Guide — Element-wise Operations — In-depth notes on Element-wise Operations with worked examples
Frequently Asked Questions
Is this the matrix exponential?
No. The matrix exponential e^A = I + A + A²/2! + ... is a matrix-valued function used in solving ODEs. This calculator applies e^x to each entry independently.
Can the output ever be negative or zero?
No. e^x > 0 for all real x, so all output entries are always positive regardless of input.
Where is element-wise exp used in practice?
The softmax function in neural networks applies exp element-wise then normalizes. It also appears in probabilistic models where parameters must be positive.