Questions tagged [transpose]

In linear algebra, the transpose of a matrix is another matrix whose i-th row and j-th column is the j-th row and i-th column of the original matrix.

In linear algebra, the transpose of a matrix A is another matrix B created by any of the below equivalent actions:

  • Reflect A over its main diagonal (which runs from top-left to bottom-right) to obtain the transpose.
  • Write the rows of A as the columns of the transpose.
  • Write the columns of A as the rows of the transpose.

This tag is to be used for questions related to the transpose operation, specifically an inquiry into its properties or special characteristics of it.

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If A and B are n×n matrices, then |A+B^T |=|A^T+B|

If $A$ and $B$ are $n×n$ matrices, then $|A+B^T|=|A^T+B|$ can I prove that it's t/f without giving a value to the matrices?
ho9
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Transposing ligand binding equation

Dear community members, I am out of school for more than 10 years and now have to transpose an equation for my work to $x$. I already tried to find a solution, but failed. I would be very grateful for some explanations. $$y = \frac{(Bx)}{(K+x)} +…
ASe1988
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How can we find the determinant of $2A^TA$ while only knowing the determinant of A and the order of the matrix?

If $A$ is a square matrix of order 3 and $det(A)=5$, then how much is $det(2A^TA)$? Assuming the product of a matrix and its transpose is nothing special how do we solve this question? This was a previous year test question so I don't think it's a…
Claritta
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Finding a matrix A such that T(A) = B

Given the linear transformation T(A) = A + A^T and B = B^T, find a matrix A such that T(A) = B A should be given in terms of A and B.
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Confusion with definition of transposed matrix using indexed familiy

Background So we have a matrix: $A = (a_{ij}) = \begin{pmatrix} a_{11} & \dots & a_{1n} \\ \vdots & & \vdots \\ a_{m1} & \dots & a_{mn} \end{pmatrix} \in K^{m \times n}$ The transposed matrx is often simply defined by $A^\mathrm{T} = (a_{ji})$. Why…
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When does this matrix have one solution, no solution, or infinitely many solutions?

Suppose I have an m x n matrix A is: Under which conditions will the (A$^{T}$A) $x$ = B have one solution, no solution, infinitely many solutions? Note: m x n can be anything. As in, we can have m>n, m
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Show that $\det\left(xB+yB^T\right)$ is a multiple of $x+y$ where $B$ be a $3\times3$ matrix

Let $B$ be a $3\times3$ matrix, and $f(x,y)= \det\left(xB+yB^T\right)$. Show that $f(x,y)$ is a multiple of $x+y$, where $x,y$ are real numbers and $B$ is any 3 by 3 matrix with real entries. I can only think of a tedious method to show this…
Anderson
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Proof: The scalar of the inverse matrix is the matrix transpose.

if I have a Scalar Matrix A then in inverse is it the same as Matrix A transpose $(kA)^{-1} = A^T $ How can I prove this property? I would appreciate it if somebody can help me.
Chris
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If A is a skew symmetric matrix such that A'A=I then A^4n-1 is equal to

Please help me to answer this question: If A is a skew symmetric matrix such that $A^TA=I$, then $A^{4n-1}=$
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Solving for Unknown in Matrix

What number $b$ in \begin{bmatrix} 3 & b \\ 1 & 0 \end{bmatrix} makes $A = Q\Lambda Q^T$ possible?
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show $A^TAx=A^Tb$ has a solution with Rank (A) not necessarily n

There is a sytem $Ax=b$ with rank A not necessarily n How to prove that $A^TAx=A^Tb$ Has a solution?
holodorum
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Which two following statements are false?

Can someone explain to me the points iii , iv and v? I understand 1 and 2, but don't get the other 3. Thank you!
cicero866
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Conjugate transpose arithmetic question

There's this really simple question that's been bugging me since I can't seem to finish it. Let $A$ be an $n\times n$ matrix with complex entries, and $A^*$ its conjugate transpose. Given $A^*=A^7$, show $A^8=I$. I tried using the property…
aaron
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Transpose of a vector: Find values to be not perpendicular

I have a question in my work where I have to find the values of a and b such that (a,2,3)^T and (1,2,b-2)^T are not perpendicular. (I have chosen random values as an example, as I'm not asking anyone to do my work for me) The way I was going to work…
Lucy
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How to find Transpose Matrix?

I know how to find the transpose matrix in case of ($2 \times 2$) dimension But I get confused when i try to find Transpose matrix incase of $(3 \times 3)$ dimension .Because i cant apply rule of ($2 \times 2$)to ($3 \times 3$). Let $$A =…
Schl....r
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