Transpose a Large Binary Matrix with Limited Memory

Early August, 2026

You are given a potentially very large matrix stored in a binary file. The file begins with a 20-byte header containing a fixed signature, the number of rows, the number of columns, and the number of bytes per element. The matrix data follows the header. Implement a transpose(name) function that reads the binary matrix and writes its transpose to a new binary file. If the input matrix has dimensions M × N, the output must have dimensions N × M, with each input element (i, j) written to output position (j, i). The output file must contain the correctly updated header followed by the transposed matrix data. You cannot use built-in transpose operations such as matrix.T or numpy.transpose; implement the transpose logic yourself. After implementing a simple correct solution, discuss how you would handle matrices much larger than available RAM (for example, 20+ GB). The follow-up focuses on an out-of-core/block-based solution: divide the matrix into tiles, load only one tile at a time, transpose it, and write it directly to its final location in the output file.