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101. Symmetric matrices
easy
Generalsenior
Work with symmetric matrices by checking whether a square matrix equals its transpose and, if it is symmetric, returning its symmetric part.
Requirements
Implement the function
python
Rules:
- Treat
Aas symmetric if the maximum absolute entry-wise difference betweenAandA^Tis at most1e-9. - Always return the symmetric part (S = \frac{1}{2}(A + A^\top)), even if
Ais not symmetric. - Input and output must be NumPy arrays.
- Keep it all inside this single function.
Example
python
Output:
python
Input Signature
| Argument | Type |
|---|---|
| A | np.ndarray |
Output Signature
| Return Name | Type |
|---|---|
| value | tuple |
Constraints
Input/output must be NumPy arrays.
Square matrix; use tolerance 1e-9.
Hint 1
Symmetry check: compare A with A.T using np.abs(A - A.T) and find the maximum difference.
Hint 2
Use the tolerance rule: is_symmetric = (max_diff <= 1e-9).
Hint 3
Compute symmetric part vectorized: S = 0.5 * (A + A.T).
Roles
ML Engineer
AI Engineer
Companies
GeneralLevels
senior
entry
Tags
matrix-transpose
numerical-tolerance
symmetric-part
nested-loops
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Python EditorLn 1, Col 1