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Transposed matrix, symmetric matrix and opposite matrix


  • Transposed Matrix: matrix At obtained from matrix A by neatly changing rows by columns or columns by rows. For example:

Thus, if the matrix THE it's like m x n, THEt is of type n x m. Note that the first line of THE corresponds to the 1st column of THEt and the 2nd row of A corresponds to the 2nd column of THEt.

  • Symmetric matrix: square matrix of order n such that A = At . For example,

is symmetrical because the12 = a21 = 5, the13 = a31 = 6, the23 = a32 = 4, ie we always have the ij = a ji.

  • Opposite Matrix: matrix -THE obtained from THE changing the signal of all the elements of THE. For example, .

Equality of matrices

Two matrices, A and B, of the same type m x n, are equal if and only if all elements occupying the same position are equal:

.

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