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unitary    音标拼音: [j'unɪt,ɛri]
a. 一个的,单一的,归一的,整体的

一个的,单一的,归一的,整体的

unitary
单一的; 单元的; 单式的; 正的

unitary
单一

unitary
adj 1: relating to or characterized by or aiming toward unity;
"the unitary principles of nationalism"; "a unitary
movement in politics"
2: of or pertaining to or involving the use of units; "a unitary
method was applied"; "established a unitary distance on which
to base subsequent calculations"
3: characterized by or constituting a form of government in
which power is held by one central authority; "a unitary as
opposed to a federal form of government" [ant: {federal}]
4: having the indivisible character of a unit; "a unitary
action"; "spoke with one voice" [synonym: {one(a)}, {unitary}]

Unitary \U"nit*a*ry\, a.
1. Of or pertaining to a unit or units; relating to unity;
as, the unitary method in arithmetic.
[1913 Webster]

2. Of the nature of a unit; not divided; united.
[1913 Webster]

{Unitary theory} (Chem.), the modern theory that the
molecules of all complete compounds are units, whose parts
are bound together in definite structure, with mutual and
reciprocal influence on each other, and are not mere
aggregations of more or less complex groups; --
distinguished from the dualistic theory.
[1913 Webster]


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  • What is the difference between isometric and unitary operators on a . . .
    A stronger notion is unitary equivalence, i e , similarity induced by a unitary transformation (since these are the isometric isomorphisms of Hilbert space), which again cannot happen between a nonunitary isometry and a unitary operator (or between any nonunitary operator and a unitary operator)
  • linear algebra - Norm preservation properties of a unitary matrix . . .
    Definition (Unitary matrix) A unitary matrix is a square matrix $\mathbf {U} \in \mathbb {K}^ {n \times n}$ such that \begin {equation} \mathbf {U}^* \mathbf {U} = \mathbf {I} = \mathbf {U} \mathbf {U}^* \end {equation} Definition (Vector $2$ -norm)
  • linear algebra - Singular value decomposition for unitary matrices . . .
    I know the title is strange, but there are many instances in quantum information in which one is interested not in diagonalizing a unitary matrix, but instead in finding its singular value decompos
  • prove that an operator is unitary - Mathematics Stack Exchange
    prove that an operator is unitary Ask Question Asked 5 years, 5 months ago Modified 5 years, 5 months ago
  • linear algebra - Whats the interpretation of a unitary matrix . . .
    Unitary matrices are the complex versions, and they are the matrix representations of linear maps on complex vector spaces that preserve "complex distances" If you have a complex vector space then instead of using the scaler product like you would in a real vector space, you use the Hermitian product
  • If H is Hermitian, show that $e^ {iH}$ is unitary
    In the case where H is acting on a finite dimensional vector space, you can essentially view it as a matrix, in which case (by for example the BCH formula) the relation you state in a) is valid More generally if $ [A,B]=0$ then the product of exponentials is just the exponential of the sum There may be subtleties in the more general case, but I doubt you'd even be interested in those As for
  • Operator - Exponential form - Mathematics Stack Exchange
    A unitary operator is a diagonalizable operator whose eigenvalues all have unit norm If we switch into the eigenvector basis of U, we get a matrix like: \begin {bmatrix}e^ {ia} 0 0\\0 e^ {ib} 0\\0 0 e^ {ic}\\\end {bmatrix} which is obviously the exponential of a diagonal hermitian matrix
  • unitary operator explanation - Mathematics Stack Exchange
    Geometrically, it turns out that every unitary transformation consists of a combination of "reflections" and "rotations" You should verify that rotations and reflections indeed satisfy the two properties listed above, i e they preserve both length and the angle between vectors
  • matrices - General form of a $4\times 4$ unitary matrix - Mathematics . . .
    I was trying to find the most general way of writing a $4\\times 4$ unitary matrix but I got stuck when I obtained a set of equations that did not look very pretty after starting from something like
  • What is the manifold structure of $U (n)$?
    The infinite-dimensional unitary group is not a manifold in the usual sense, although it is a Hilbert manifold Kuiper's theorem implies that it is weakly contractible, so from the perspective of homotopy theory it looks like a point





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