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The Transpose of a Matrix
The 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.
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What does transpose mean in math?
Transpose means swap places. In maths, the term is usually used for matrices. It means truning the matrix around so that its rows become columns and columns become rows.
What is the definition of a null matrix?
The null matrix is also called the zero matrix. It is a matrix with 0 in all its entries.
What is the definition of outcome in regards to math?
the answer to a math question.
What is the definition of a trace of a 3 3 matrix?
The trace of a 3 by 3 matrix A is defined as the summation of n=3;i=1;aii.
A is a 3 x 4 matrix what is its transpostion?
If A is a 3x4 matrix with values ([a11, a12, a13, a14], [a21, a22, a23, a24], [a31, a32, a33, a34]) then its transpose AT is a 4x3 matrix values with its values changed diagonally like so, ([a11, a21, a31], [a12, a22, a32], [a13, a23, a33], [a14, a24, a34])
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 a matrix?
Symmetric Matrix:Given a square matrix A such that A'=A, where A' is the transpose of A, then A is a symmetric matrix.note: No need to think about diagonal elements, they can be anything.
what is the definition of The Matrix?
Symmetric Matrix:Given a square matrix A such that A'=A, where A' is the transpose of A, then A is a symmetric matrix.note: No need to think about diagonal elements, they can be anything.
What is the definition of a symmetric matrix?
Symmetric Matrix:Given a square matrix A such that A'=A, where A' is the transpose of A, then A is a symmetric matrix.note: No need to think about diagonal elements, they can be anything.
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.
What is a symmetric matrix?
a square matrix that is equal to its transpose
What is transpose of the sparse matrix?
Another sparse matrix.
Is the row space of matrix an equivalent to the column space of matrix AT which is the transpose of matrix A?
Since the columns of AT equal the rows of A by definition, they also span the same space, so yes, they are equivalent.
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.
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.
