Transpose Matrix

Transpose Matrix

What is this problem about?

The "Transpose Matrix coding problem" is a fundamental matrix operation. Given a 2D integer array matrix, you need to return its transpose. The transpose of a matrix is obtained by flipping it over its main diagonal, which effectively switches the row and column indices of every element. For an $m \times n$ matrix, the resulting transpose will have dimensions $n \times m$.

Why is this asked in interviews?

This "Transpose Matrix interview question" is a common "warm-up" problem for companies like Apple, Microsoft, and Meta. It verifies that a candidate can work with 2D arrays, nested loops, and understands the basics of linear algebra representations in code. It's a simple test of "coding hygiene"—can you handle the index boundaries correctly when the matrix is not square?

Algorithmic pattern used

The "Array, Matrix, Simulation interview pattern" involves creating a new 2D array of the target dimensions ($n \times m$). We then iterate through the original matrix using a nested loop: for each element at matrix[r][c], we place it at result[c][r]. This is a straightforward $O(m \times n)$ operation in both time and space.

Example explanation

Input:

[[1, 2, 3],
 [4, 5, 6]]

Dimensions: 2 rows, 3 columns. Transposed dimensions: 3 rows, 2 columns.

1. Element at [0,0] (1) -> result[0,0]
2. Element at [0,1] (2) -> result[1,0]
3. Element at [0,2] (3) -> result[2,0]
4. Element at [1,0] (4) -> result[0,1]
5. ...and so on. Output:

[[1, 4],
 [2, 5],
 [3, 6]]

Common mistakes candidates make

The most frequent mistake in the "Transpose Matrix coding problem" is attempting to transpose the matrix "in-place" when it is not square. In-place transposition is only simple for $n \times n$ matrices; for rectangular matrices, it is extremely complex and usually requires a new array. Another error is confusing the loop limits, which leads to IndexOutOfBounds exceptions when accessing the columns of the original matrix as rows of the new one.

Interview preparation tip

For the "Array, Matrix, Simulation interview pattern," always double-check your loop boundaries. A good tip is to name your variables clearly (e.g., numRows, numCols, r, c) to avoid mixing up indices. Practice this alongside other matrix operations like rotation or spiral traversal.