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Transposing a matrix is O(n*m) where m and n are the number of rows and columns. For an n-row square matrix, this would be quadratic time-complexity.
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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.
What is a fast-transpose algorithm for sparse matrices?
A fast-transpose is a computer algorithm that quickly transposes a sparse matrix using a relatively small amount of memory. Using arrays normally to record a sparse matrix uses up a lot of memory since many of the matrix's values are zero. In addition, using the normal transpose algorithm to transpose this matrix will take O(cols*elements) amount of time. The fast-transpose algorithm only uses a little memory to record the matrix and takes only O(cols+elements) amount of time, which is efficient considering the number of elements equals cols*rows.
How do you find transportation of matrix?
Invert rows and columns to get the transpose of a matrix
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 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]; } } }
Why transpose of a matrix is orthogonal?
It need not be, so the question makes no sense!
What is the definition of unitary matrix?
It is the conjugate transpose of the matrix. Of course the conjugate parts only matters with complex entries. So here is a definition:A unitary matrix is a square matrix U whose entries are complex numbers and whose inverse is equal to its conjugate transpose U*. This means thatU*U = UU* = I. Where I is the identity matrix.
