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canonic

canonic, a. (and n.) (kəˈnɒnɪk) [ad. L. canonic-us, = Gr. κανονικός of or according to canon2; or a. F. canonique. Already in OE. as n. = modern canon n.2] A. adj. 1. Authorized by, or according to, ecclesiastical canons; = canonical 1.1483 Caxton Gold. Leg. 219/1 Euery day atte vii houres canonyque... Oxford English Dictionary

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Canonic Trio Sonata in F major, BWV 1040

The Canonic Trio Sonata in F major is a short piece by Johann Sebastian Bach, catalogued as BWV 1040. wikipedia.org

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canonico-

caˈnonico- combining form of canonic.1689 Apol. Fail. Walker's Acc. 25 It being Canonico-Prelatically impossible, tho Schismatico-Presbyterially certain. Oxford English Dictionary

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Canonic Variations on "Vom Himmel hoch da komm' ich her"

It makes sense to place the faster canonic voice in the upper manual and the longer canonic one in the lower manual, with the free alto voice also in the Reception The Canonic Variations were among the works included in J. G. wikipedia.org

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Canonic form of A matrix defined by a condition of powers equation I have to solve this old exam problem: A square matrix $A$ of order $4$ is not diagonalisable and satisfy this condition: $(A−I)^4 = 4(A−I)^2 = 9(A−...

So the minimal polynomial is: $m\substack{A}(t)=(t-1)^2$ And the possible canonic form are: $J\substack{1}=\begin{bmatrix}1&1&0&0\\\0&1&0&0\\\0&0&1&1

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Canonic identification $T_{I_n}\mathfrak{gl}(n,\mathbb{R}) \rightarrow \mathfrak{gl}(n,\mathbb{R}) $ I am currently studying Lie Groups and have a questions about this: Let $x_{ij} : M_n(\mathbb{R}) \rightarrow \math...

I think what is meant is that for a vector space $V$ (such as $\mathfrak{gl}(n,\mathbb R)$), and a point $x\in V$, there is a natural identification of $T_xV$ with $V$. From your comment I take it that you prefer to view tangent vectors as operators on functions. In this language, the identification...

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Missa sine nomine (Josquin)

It is one of Josquin's only masses not to be based on pre-existing material, and like the Missa ad fugam, it is a canonic mass. Josquin wrote only two canonic masses, the Missa ad fugam and the Missa sine nomine; they seem to stand at opposite ends of his career, and in the latter wikipedia.org

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Canonic form of a quadric I have a question, how can determine the canonic form of the quadric associated to $F$, where $F$ is a bilinear form $\Bbb R^3\times\Bbb R^3\to\Bbb R $ that its associated matrice is $A=\left...

The quadratic form associated to $F$ is $x^TAx$ and since $A$ is symmetric by spectral theorem $A$ can be diagonalized by a basis of orthogonal eigenvectors $v_1,v_2,v_3$ that is $$M=[v_1\,v_2\,v_3] \implies x=My\quad M^{-1}=M^T$$ and then $x^TAx=(My)^TA(My)=y^TM^TAMy=y^T(M^{-1}AM)y=y^TDy=\lambda_1y...

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卡农

Canons and Canonic Techniques, 14th–16th Centuries: Theory, Practice, and Reception History. Canonic Studies: A New Technique in Composition, edited and introduced by Ronald Stevenson. New York: Crescendo Pub., 1977. . wikipedia.org

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Naturality of Riesz' Representation What does it mean precisely in the context of category theory when somebody says that Riesz' representation is canonic resp. every Hilbert space is naturally antiisomorphic ...

This is a very interesting issue. In fact, this isomorphism is _not_ as "natural" as one might have thought. As an exercise, one should see that, given a map of Hilbert spaces $V\to W$ it is rarely the case that the square of maps involving $W^*\to V^*$ and the "Riesz-Fisher" dualities ... commutes....

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Kernel of the quadratic form $q(x,y,z)=3x^2+6xy+10xz+2yz+3z^2$ Let $q:\mathbb{R^3} \to \mathbb{R}$ such that $$q(x,y,z)=3x^2+6xy+10xz+2yz+3z^2.$$ I have to determine rank, signature, kernel, and the canonic form of q ...

You should have got without problems that $$q(x,y,z) = \begin{pmatrix} x & y & z \end{pmatrix}\begin{pmatrix} 3 & 3 & 5 \\\ 3 & 0 & 1 \\\ 5 & 1 & 3\end{pmatrix}\begin{pmatrix}x \\\ y \\\ z\end{pmatrix}.$$ Call $Q$ that middle matrix. Note that $\det Q = -3 -3(4)+5(3) = 0$, but the minor $$\begin{pma...

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Orthogonal projection on the image of a linear operator Let $f: \mathbb{R}^n \to \mathbb{R}^n$ be a linear operator whose corresponding matrix $A$ (with respect the canonic bases in both the domain and the codomain) i...

**Hint** : If $A^2=A$ then $A(A-1) \in I(A)$ so the matrix is diagonalizable with eigenvalues $0,1$. Let's now represent this diagonalized matrix: $$J=\begin{pmatrix} 1 \\\ &\ddots \\\ &&1 \\\ &&&0 \\\ &&&&\ddots \\\&&&&&0\end{pmatrix}$$ What does this matrix to your vector when you do $J(v), v\in V...

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ONS in Prehilbert space Suppose $a:=\left(\frac{1}{j}\right)_{j \in \mathbb{N}}$ and $e_n$ be the canonic unit vector in $l^2$. The prehilbert space $H \subset l^2$ is defined as the linear span of the vectors $\lbrac...

I assume you want $H=\operatorname{span}\\{a,e_2,e_3,\ldots\\}$. Otherwise, $x=e_1$ makes your second statement false. The set $\\{e_n\\}_{n\geq2}$ is not a basis because $\langle a,e_n\rangle=1/n\ne0$. Any element $x$ of $H$ is of the form $$ x=x_1 a+\sum_{n\geq2} x_ne_n=x_1e_1+\sum_{n\geq2}(x_n+\f...

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Infimum of this expression Let $n \in \mathbb{N}$ and $r_1, \dots, r_n$ be positive real numbers. Is it true that $$ \inf \left\lbrace r_1 x_1 + \cdots + r_n x_n : x = (x_1, \dots, x_n) \in \mathbb{R}^n, \, x_i \geq...

Let $R = \min \\{r_i : 1 \le i \le n\\}$. If each $x_i \ge 0$ and $\sum_{i=1}^n x_i^2 = 1$ then each $x_i$ satisfies $0 \le x_i \le 1$. In particular, $x_i^2 \le x_i$ for each index $i$. For any $n$-tuple of such $x_i$'s you get $$r_1x_1 + \cdots + r_nx_n \ge R (x_1 + \cdots + x_n) \ge R (x_1^2 + \c...

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show that any orbit that intercepts the unitary sphere $S^{n-1}$ is contained in it also Let $X : U \rightarrow R^n$ a vector field such that $ \langle X(p); p \rangle = 0 \,\,\,\,\,\,\,\,\ \forall p \in R^n; \,\,\,\...

Lets consider the integral curve $\gamma: I \to \mathbb R^n$ of the vector field $X$, where $I$ is an interval. That is, $\gamma'(t) = X(\gamma(t))$ for all $t\in I$. Suppose $|\gamma(t_0)|=1$ for some $t_0 \in I$. We want to show that $|\gamma(t)|=1$ for all $t\in I$. Consider $f(t) = \langle \gamm...

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canonic

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canonic

Canonic Trio Sonata in F major, BWV 1040

canonico-

Canonic Variations on "Vom Himmel hoch da komm' ich her"

Canonic form of A matrix defined by a condition of powers equation I have to solve this old exam problem: A square matrix $A$ of order $4$ is not diagonalisable and satisfy this condition: $(A−I)^4 = 4(A−I)^2 = 9(A−...

Canonic identification $T_{I_n}\mathfrak{gl}(n,\mathbb{R}) \rightarrow \mathfrak{gl}(n,\mathbb{R}) $ I am currently studying Lie Groups and have a questions about this: Let $x_{ij} : M_n(\mathbb{R}) \rightarrow \math...

Missa sine nomine (Josquin)

Canonic form of a quadric I have a question, how can determine the canonic form of the quadric associated to $F$, where $F$ is a bilinear form $\Bbb R^3\times\Bbb R^3\to\Bbb R $ that its associated matrice is $A=\left...

卡农

Naturality of Riesz' Representation What does it mean precisely in the context of category theory when somebody says that Riesz' representation is canonic resp. every Hilbert space is naturally antiisomorphic ...

Kernel of the quadratic form $q(x,y,z)=3x^2+6xy+10xz+2yz+3z^2$ Let $q:\mathbb{R^3} \to \mathbb{R}$ such that $$q(x,y,z)=3x^2+6xy+10xz+2yz+3z^2.$$ I have to determine rank, signature, kernel, and the canonic form of q ...

Orthogonal projection on the image of a linear operator Let $f: \mathbb{R}^n \to \mathbb{R}^n$ be a linear operator whose corresponding matrix $A$ (with respect the canonic bases in both the domain and the codomain) i...

ONS in Prehilbert space Suppose $a:=\left(\frac{1}{j}\right)_{j \in \mathbb{N}}$ and $e_n$ be the canonic unit vector in $l^2$. The prehilbert space $H \subset l^2$ is defined as the linear span of the vectors $\lbrac...

Infimum of this expression Let $n \in \mathbb{N}$ and $r_1, \dots, r_n$ be positive real numbers. Is it true that $$ \inf \left\lbrace r_1 x_1 + \cdots + r_n x_n : x = (x_1, \dots, x_n) \in \mathbb{R}^n, \, x_i \geq...

show that any orbit that intercepts the unitary sphere $S^{n-1}$ is contained in it also Let $X : U \rightarrow R^n$ a vector field such that $ \langle X(p); p \rangle = 0 \,\,\,\,\,\,\,\,\ \forall p \in R^n; \,\,\,\...