Matrix transposition is the operation of flipping a matrix over its diagonal, effectively switching the row and column indices of each element. This process transforms a matrix A with dimensions m x n into a new matrix A^T with dimensions n x m, where each element at position (i, j) in A moves to position (j, i) in A^T. Transposing is crucial in various mathematical applications, including solving linear equations, optimizing calculations in tensor representation, and manipulating data structures in computer science.
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