# Transpose

Transpose is a common operation in matrix math and most computer languages that work with matrices. Transpose rearranges a square matrix A[i, j] by exchanging rows and columns, so the transpose matrix A'[i, j] = A[j, i]. The main reason for transposing a matrix is to make sure that matrix operations match up rows and columns.

In Analytica, each dimension of an array or matrix is labeled by an Index. When viewing the array as a table, you can select which index to show down rows or across columns simply by pivoting it, according to which view you find most useful. Analytica uses the Indexes to match up indexes when doing operations on matrices.

However there are occasional circumstances in which you might want to exchange two indexes in a square matrix. Suppose you have a matrix A indexed by I and J, each with the same length.

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