Transpose Matrix Mathematica

For example a 4 1.

Transpose matrix mathematica. Hermitian matrices are a useful generalization of symmetric matrices for complex matrices a matrix m can be tested to see if it is symmetric using the. For a square matrix m transpose m 1 1 returns the main diagonal of m as given by diagonal m. Mathematica the 1 tool for creating demonstrations and anything. Conjugatetranspose m or m conjugatetranspose gives the conjugate transpose of m.

The way transposing a vector was explained to me in linear algebra was that we may consider a vector as a either a row matrix or a column matrix which may be transposed. Revolutionary knowledge based programming language. If is an matrix then is an matrix. Endgroup michael e2 jan 1 15 at 18 32.

Transpose allows the n i to be repeated computing diagonals of the subarrays determined by the repeated levels. To transpose a matrix start by turning the first row of the matrix into the first column of its transpose. The matrix transpose most commonly written is the matrix obtained by exchanging s rows and columns and satisfies the identity 1 unfortunately several other notations are commonly used as summarized in the following table. The result is therefore an array of smaller depth.

Repeat this step for the remaining rows so the second row of the original matrix becomes the second column of its transpose and so on. A symmetric matrix is a square matrix that satisfies a t a 1 where a t denotes the transpose so a ij a ji. 1 2 3 is a symmetric matrix. Write the columns of as the rows of write the rows of as the columns of take the element of as the element of reflect over its main diagonal which runs top left to bottom right to obtain.

This also implies a 1 a t i 2 where i is the identity matrix. This transposition is the same for a square matrix as it is for a non square matrix. In mathematica a row matrix has the form 1 1 1 1 as sungmin points out.