por Do you know what a transposed matrix is and how to identify it? In this article we will teach you what this concept refers to, which becomes relevant in the world of computing when we combine it with machine learning.
Transposed matrix
Given a matrix A of mxnthe transpose of A is the matrix nxmdenoted by ATwhose columns are formed from the corresponding rows of A. In summary, The transposed matrix is the one obtained by transforming the rows into columns and the columns into rows.. This is done as follows:
Transposed matrix
We have here an example with 2 rows by 3 columns (2×3). Your transposed matrix is to take the first row and turn it into a column. That is, the first row [5, 1, 7] would be converted into a column [5, 1, 7]. The same would be done with the second row. [3, -2, 5]which would become a column of the same type.
We can do this in Python using np.transpose() to calculate the transpose of a matrix A:
#Transposed array A = np.array ([[5, 1, 7],
[3, -2, 5]]) At = np.transpose (A) print (At)
[[5 3]
[1 -2]
[7 5]]
What happens if we do the transposition again?
#Transposed matrix att = np.transpose(At) print(Att)
[[5, 1, 7]
[3, -2, 5]]
We obtain matrix A again, as expected. Here what we have done is transform the first row [5 3]the second row [1 -2] and the third row [7 5] in columns, respectively.
square matrix
A square matrix will be symmetric if AT= A, that is, if A is equal to its own transposed matrix. For example:
#Square matrix/transposed matrix C = np.array ([[126, -66, 88],
[-66, 58, -50],
[88, -50, 46]]) Ct = np.transpose (C) Ct
array (
[[126, -66, 88],
[-66, 58, -50],
[88, -50, 46]])
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