Mathematics Stack Exchange
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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.

579 questions
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Transpose of obvious inclusion map surjective?

I was wondering if the in the title mentioned statement is true or false? I thought I read about it but I'm not sure if it's true and provable or not. So if we have $V$ a K-vector space and $U \subset V$ a subspace. We take $\phi$: $U \to V$ as the…
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a proof regarding ordinary least squares

I am reading a statistics textbook. On page 271, in the section 'a brief derivation', the author proves a theorem about the ordinary least squares method. He proves that the size of error is minimized, when the error vector $\vec{\epsilon}$ is…
Nownuri
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How to define or uniquely identify transpose without referring to "swapping cells of matrix"?

Is there a way to pick out the transpose $\lambda M \mathop. M^T$ (with $\lambda$ denoting an anonymous function) from the automorphisms of linear transformations from $\mathbb{R}^n$ to $\mathbb{R}^n $, or, equivalently, linear transformations of…
Greg Nisbet
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How to modify a formula to suit this application

I have an problem that I am unsure how to solve. Hopefully someone can edit this question to get the fancy equations up as I don't know how. I have a formula to find a variable, say $$a = \frac{(b * c)} {d}$$ Now if d = 1000 but due to my…
David777
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Transpose of $Y ={A}^{*} \operatorname{diag} \left( b \right) {A} $

What would the tranpose of $Y$ look like $$Y ={A}^{*} \operatorname{diag} \left( b \right) {A} $$ where $*$ is the conjugate tranpose, i.e., hermitian.
abina shr
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from time per revolution to revolutions per time

I am counting how long it takes for a motor to make one revolution, and I would like to express that as revolutions per minute. "Normally" one would count the revolutions made in one second, and multiply that up to revolutions per minute. However…
AhBajeezus
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transpose formula when x is power of n

I need help transposing this formula to solve for F0. the problem is that i don't know what to do when Octave is > 2. Apologies if this is a noob question :P $S_n$ = $\dfrac{F0-2^{Octave} \times 20}{(2^{Octave} \times 20)/12}$
Evgeny Danilenko
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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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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 $A^{4n-1}=$
Priyansh Mehta
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