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What is a symmetric matrix?
a square matrix that is equal to its transpose
What is the meaning of transpose?
The transpose of a matrix A is the matrix B that is obtained by swapping the rows and columns of A into the columns and rows of B. In algebraic form, if A = {aij} then B = {aji} is its transpose, where 1 ≤ i ≤ n and 1 ≤ j ≤ m.
What is an adjoint matrix?
The classical adjoint of a square matrix A the transpose of the matrix who (i, j) entry is the a i j cofactor.
Why transpose of a matrix is orthogonal?
It need not be, so the question makes no sense!
What is an orthogonal matrix?
A matrix A is orthogonal if itstranspose is equal to it inverse. So AT is the transpose of A and A-1 is the inverse. We have AT=A-1 So we have : AAT= I, the identity matrix Since it is MUCH easier to find a transpose than an inverse, these matrices are easy to compute with. Furthermore, rotation matrices are orthogonal. The inverse of an orthogonal matrix is also orthogonal which can be easily proved directly from the definition.
Is it true that the transpose of the transpose of a matrix is the original matrix?
yes, it is true that the transpose of the transpose of a matrix is the original matrix
What is the definition of transpose in regards to a matrix?
The Transpose of a MatrixThe matrix of order n x m obtained by interchanging the rows and columns of the m X n matrix, A, is called the transpose of A and is denoted by A' or AT.
What is a symmetric matrix?
a square matrix that is equal to its transpose
What is transpose of the sparse matrix?
Another sparse matrix.
How can one find a unitary matrix?
To find a unitary matrix, one must first square the matrix and then take the conjugate transpose of the result. If the conjugate transpose of the squared matrix is equal to the identity matrix, then the original matrix is unitary.
How do you find transportation of matrix?
Invert rows and columns to get the transpose of a matrix
Are adjoint and transpose the same?
No, adjoint and transpose are not the same, although they are related concepts in linear algebra. The transpose of a matrix is obtained by flipping it over its diagonal, while the adjoint (or adjugate) refers to the transpose of the cofactor matrix. In the context of complex matrices, the adjoint often refers to the conjugate transpose, which combines both the transpose and complex conjugation.
What is the meaning of transpose?
The transpose of a matrix A is the matrix B that is obtained by swapping the rows and columns of A into the columns and rows of B. In algebraic form, if A = {aij} then B = {aji} is its transpose, where 1 ≤ i ≤ n and 1 ≤ j ≤ m.
What is an adjoint matrix?
The classical adjoint of a square matrix A the transpose of the matrix who (i, j) entry is the a i j cofactor.
What is the algorithm to generate transpose of given matrix?
To generate the transpose of a given matrix, you can swap its rows and columns. For a matrix ( A ) with dimensions ( m \times n ), the transpose ( A^T ) will have dimensions ( n \times m ). Specifically, the element at position ( (i, j) ) in matrix ( A ) becomes the element at position ( (j, i) ) in matrix ( A^T ). This can be achieved using a nested loop that iterates through the original matrix and assigns values to the transposed matrix accordingly.
What is harmitian matrix?
Hermitian matrix (please note spelling): a square matrix with complex elements that is equal to its conjugate transpose.
Algorithm for transpose of matrix?
transpose(Matrix mat,int rows, int cols ){ //construction step Matrix tmat; for(int i=0;i<rows;i++){ for(int j=0;j<cols;j++){ tmat[j][i] = mat[i][j]; } } }
