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Matrix Trace

Linear Algebra

Easy

Compute the trace of a square matrix, which is the sum of its main-diagonal entries:

\operatorname{tr}(A)=\sum_{i=1}^{N}A_{ii}

Here, $A$ is an $N\times N$ matrix and $A_{ii}$ is its entry in row $i$ and column $i$ . Compute the sum directly from indexed elements and return it as a Python float.

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Examples

Input: A = [[1, 2], [3, 4]]

Output: 5

Explanation: The main diagonal contains 1 and 4.

Input: A = [[2, -1, 0], [3, 5, 1], [0, 2, -2]]

Output: 5

Input: A = [[42]]

Output: 42

Hint 1

Accumulate A[i, i] for i from zero through A.shape[0] - 1.

Hint 2

Convert the final NumPy scalar with float(total).

Requirements

Sum the entries whose row and column indices are equal
Do not use np.trace or np.diagonal
Return a Python float

Constraints

A is a nonempty square numeric matrix
Matrix entries may be integers or floating-point values
Use NumPy only

Try Similar Problems

Matrix Transpose Matrix Inverse Eigenvalues Make Diagonal Matrix Normalization

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Matrix Trace

Linear Algebra

Easy

Compute the trace of a square matrix, which is the sum of its main-diagonal entries:

\operatorname{tr}(A)=\sum_{i=1}^{N}A_{ii}

Here, $A$ is an $N\times N$ matrix and $A_{ii}$ is its entry in row $i$ and column $i$ . Compute the sum directly from indexed elements and return it as a Python float.

Loading visualization...

Examples

Input: A = [[1, 2], [3, 4]]

Output: 5

Explanation: The main diagonal contains 1 and 4.

Input: A = [[2, -1, 0], [3, 5, 1], [0, 2, -2]]

Output: 5

Input: A = [[42]]

Output: 42

Hint 1

Accumulate A[i, i] for i from zero through A.shape[0] - 1.

Hint 2

Convert the final NumPy scalar with float(total).

Requirements

Sum the entries whose row and column indices are equal
Do not use np.trace or np.diagonal
Return a Python float

Constraints

A is a nonempty square numeric matrix
Matrix entries may be integers or floating-point values
Use NumPy only

Try Similar Problems

Matrix Transpose Matrix Inverse Eigenvalues Make Diagonal Matrix Normalization

Case 1

Case 2

Case 3

A =

Accepts: array