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.
594 questions
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Functions of transpositions of symmetric group
The following is from Orthogonal Polynomials of Several Variables by Charles F Dunkl and Yuan Xu 2nd edition , Encyclopedia of math..and applications 155 page 320. Here i am assuming (i,j) means the ...
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Transposition of Matrices
My question concerns understanding the transpose as an operator acting on the dual of a space rather than on the space itself. This is a paraphrased version of Chapter 4 in Linear Algebra by Lax. Let $...
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Properties of a matrix such that $A+A^T= \alpha Id$ [closed]
What can be said about the properties of an $n\times n$ invertible matrix $A$ with real entries such that $A+A^T=\alpha I_n$, where $\alpha\in \mathbb{R}$? Particularly, I am looking for properties ...
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Binary matrix function that always results in transpose after composition
I have written an algorithm in MATLAB that takes a matrix, $X$, as input and produces a matrix $Y$ as output. I will call the algorithm $f$, and say that $f(X)=Y$. Both $X$ and $Y$ are binary $n \...
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What is the (geometric) intuition of the matrix transpose?
There are a lot of discussions on the matrix transpose already, but none of them seem to give a satisfying (visual) intuition. I guess I have collected the most, if not even all, ways to view and ...
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Find matrix given matrix times its transpose
I thought of this problem: How would you find a matrix A such that: AAᵀ= [14 0 12] [0 5 0] [12 0 16]? I've tried multiplying a matrix A with entries a, b, c, d, ...
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Definition and properties of a transpose map on an arbitrary Hilbert space $H$.
I am given the following definition and remark in my book: Definition: Let $A$ be a $C^{*}$-algebra and $\phi: A \rightarrow B(H)$. We say that $\phi$ is copositive if $t \circ \phi$ is completely ...
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Adjoint and transpose operator in linear algebra
Apology if this is silly or too simple. But I just realized I can't hammer out a confusion over what "adjoint" or "transpose" is supposed to mean. Suppose $X$ is an $n$-dim $k$-...
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Transposition operator is continuous? (topology of bounded convergence)
Given a continuous map of TVS $u:E\to F$, we can associate to it the transpose map $u^t:F'\to E'$. Here, $E',F'$ are the continuous duals of $E,F$, respectively. The map $u^t$ is continuous, so long ...
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Existence of the pre transpose of an ultraweakly continuous linear map between duals
I found a result in a book that seemed well known but i can't prove it. Here it is. Let $X, Y$ be two normed, complete TVS. Given an ultraweakly continuous (or weak* continuous) linear map $F : Y^* \...
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Proof that the Dual Transformation of a Dual Transformation is Itself
Let $A$ be an invertible linear transformation in $\mathbb{R}^{n\times n}$. Then, we know that $A$ takes $\mathbb{R}^{n-1}$ hyperplanes in its domain to $\mathbb{R}^{n-1}$ hyperplanes in its image. ...
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Proof of transposed matrix related equation with Levi-Civita symbol
I would like to prove the following equation in relation to Levi-Civita symbol but I got stuck: $$\left|{A^T}\right|=\left|{A}\right|, \tag{1}$$ where $A$ is a square matrix of size $3$. I am also ...
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Proof about Hadamard matrices that $H H^\textsf{T} = n I_n$ [closed]
I have read the Wikipedia article about Hadamard matrices that says: Let $H$ be a Hadamard matrix of order $n$, the following is true: $H H^\textsf{T} = n I_n$, where $I_n$ is the identity $n×n$ ...
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Product of Conjugate Transpose with Itself equalling the Zero Matrix. [duplicate]
I am reading a linear algebra book and I am stuck on one of the questions that asks to (a) : Find all nxn matrices with real entries such that $$ A^{T}A = 0 $$ (b) : Find all nxn matrices with complex ...
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Find a matrix $Q$ that has $Q(Q^T)=I$ but does not have orthonormal columns
My textbook says that if a matrix $Q$ is square and has orthonormal columns then $Q(Q^T)=I$, but it does not say the opposite (that if $Q(Q^T)=I$ then $Q$ has orthonormal columns). Is there an example ...
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