# Questions tagged [orthogonality]

This tag can be used to refer to the orthogonality of a set of vectors, a matrix or a linear transformation.

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### Where I went wrong in this chain of arguments - Linear algebra

Let $AB = I_n$. $A$ and $B$ are nonsingular, square matrices of size $n$. Let $A_{r1}$ be the first row of $A$. The products $A_{r1} B_j = 0, j \in \{2,\dots,N\}$. $B_j$ is the $j^{th}$ column of $B$. ...
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### How to prove the form of the functions which are symmetric with respect set?

Let $G$ be any set of orthogonal linear transformations of $R^{n}$ onto itself. A function $f$ is said to be symmetric with respect to $G$ if $$f(A x)=f(x), \quad \forall x, \quad \forall A \in G .$$...
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### Is there a formula for the norm of an orthogonal projection?

In all introductory linear algebra texts there is a discussion on orthogonal projection. Let $u = w_1 + w_2$, where $w_1$ is the projection of $u$ along $v$ and $w_2$ is projection of orthogonal to $v$...
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### It is known that the line doesn’t pass through the origin, what is projection of vector $\vec{a}$ onto line L

Question : Let $L$ have a vector from $\vec{x}$ = t $\begin{bmatrix} -1 \\ 1\end{bmatrix}$ + $\begin{bmatrix} 0 \\ 1\end{bmatrix}$, and let $\vec{a}$ = $\begin{bmatrix} 2 \\ 6\end{bmatrix}$...
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### Gram Schmidt process against orthogonal basis W

Another question that has a wrong answer from people adopting it. Am I wrong or the textbook wrong? Answer from book: My ans using the Gram-Schmidt process: such that $\vec{x_1} and \vec{x_2}$ are ...
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### Understanding orthogonal projection of $\vec{y}$ on to span of orthogonal set, with an example

This is to verify if there's an issue with my understanding or if there's issue with the textbook. There seem to be also a previous question here on exactly the same, hoping to help myself and future ...
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### Approximate orthogonality between two sets of Hermite functions.

Consider the set of Hermite functions $\{\phi_{n}(x,\varepsilon_{1})\}_{n}:= A$ defined below. \label{eqn:funcs} \phi_{n}(x,\varepsilon_{1}) = \frac{\sqrt[8]{1+\big(\frac{2\...
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### How to compare orthogonal vectors?

I doubt if I am asking this question correctly but for what it’s worth I have a set of orthogonal vectors for which I would like to pick from another set the closest orthogonal vector from it to my ...
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