Home U+2100 to U+214F Letterlike Symbols
Glyph for U+210D
Source: Noto Sans

U+210D DOUBLE-STRUCK CAPITAL H

U+210D was added to Unicode in version 1.1 (1993). It belongs to the block U+2100 to U+214F Letterlike Symbols in the U+0000 to U+FFFF Basic Multilingual Plane.

This character is a Uppercase Letter and is commonly used, that is, in no specific script.

The glyph is a Font composition of the glyph Glyph for U+0048 Latin Capital Letter H. It has a Neutral East Asian Width. In bidirectional context it acts as Left To Right and is not mirrored. The glyph can, under circumstances, be confused with 1 other glyphs. In text U+210D behaves as Alphabetic regarding line breaks. It has type Upper for sentence and Alphabetic Letter for word breaks. The Grapheme Cluster Break is Any.

The Wikipedia has the following information about this codepoint:

In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. Hamilton defined a quaternion as the quotient of two directed lines in a three-dimensional space, or, equivalently, as the quotient of two vectors. Multiplication of quaternions is noncommutative.

Quaternions are generally represented in the form

a + b   i + c   j + d   k {displaystyle a+b mathbf {i} +c mathbf {j} +d mathbf {k} }

where a, b, c, and d are real numbers; and i, j, and k are the basic quaternions.

Quaternions are used in pure mathematics, but also have practical uses in applied mathematics, particularly for calculations involving three-dimensional rotations, such as in three-dimensional computer graphics, computer vision, and crystallographic texture analysis. They can be used alongside other methods of rotation, such as Euler angles and rotation matrices, or as an alternative to them, depending on the application.

In modern mathematical language, quaternions form a four-dimensional associative normed division algebra over the real numbers, and therefore a ring, being both a division ring and a domain. The algebra of quaternions is often denoted by H (for Hamilton), or in blackboard bold by H . {displaystyle mathbb {H} .} It can also be given by the Clifford algebra classifications Cl 0 , 2 ⁡ ( R ) ≅ Cl 3 , 0 + ⁡ ( R ) . {displaystyle operatorname {Cl} _{0,2}(mathbb {R} )cong operatorname {Cl} _{3,0}^{+}(mathbb {R} ).} In fact, it was the first noncommutative division algebra to be discovered.

According to the Frobenius theorem, the algebra H {displaystyle mathbb {H} } is one of only two finite-dimensional division rings containing a proper subring isomorphic to the real numbers; the other being the complex numbers. These rings are also Euclidean Hurwitz algebras, of which the quaternions are the largest associative algebra (and hence the largest ring). Further extending the quaternions yields the non-associative octonions, which is the last normed division algebra over the real numbers. (The sedenions, the extension of the octonions, have zero divisors and so cannot be a normed division algebra.)

The unit quaternions can be thought of as a choice of a group structure on the 3-sphere S3 that gives the group Spin(3), which is isomorphic to SU(2) and also to the universal cover of SO(3).

Representations

System Representation
8461
UTF-8 E2 84 8D
UTF-16 21 0D
UTF-32 00 00 21 0D
URL-Quoted %E2%84%8D
HTML-Escape ℍ
Wrong windows-1252 Mojibake ℍ
HTML-Escape ℍ
HTML-Escape ℍ
LATEX \mathbb{H}

Related Characters

Confusables

Elsewhere

Complete Record

Property Value
Age 1.1 (1993)
Unicode Name DOUBLE-STRUCK CAPITAL H
Unicode 1 Name DOUBLE-STRUCK H
Block Letterlike Symbols
General Category Uppercase Letter
Script Common
Bidirectional Category Left To Right
Combining Class Not Reordered
Decomposition Type Font
Decomposition Mapping Glyph for U+0048 Latin Capital Letter H
Lowercase
Simple Lowercase Mapping Glyph for U+210D Double-Struck Capital H
Lowercase Mapping Glyph for U+210D Double-Struck Capital H
Uppercase
Simple Uppercase Mapping Glyph for U+210D Double-Struck Capital H
Uppercase Mapping Glyph for U+210D Double-Struck Capital H
Simple Titlecase Mapping Glyph for U+210D Double-Struck Capital H
Titlecase Mapping Glyph for U+210D Double-Struck Capital H
Case Folding Glyph for U+210D Double-Struck Capital H
ASCII Hex Digit
Alphabetic
Bidi Control
Bidi Mirrored
Bidi Paired Bracket Glyph for U+210D Double-Struck Capital H
Bidi Paired Bracket Type None
Cased
Composition Exclusion
Case Ignorable
Full Composition Exclusion
Changes When Casefolded
Changes When Casemapped
Changes When NFKC Casefolded
Changes When Lowercased
Changes When Titlecased
Changes When Uppercased
Dash
Deprecated
Default Ignorable Code Point
Diacritic
East Asian Width Neutral
Emoji Modifier Base
Emoji Component
Emoji Modifier
Emoji
Emoji Presentation
Extender
Extended Pictographic
FC NFKC Closure Glyph for U+0068 Latin Small Letter H
Grapheme Cluster Break Any
Grapheme Base
Grapheme Extend
Grapheme Link
Hex Digit
Hangul Syllable Type Not Applicable
Hyphen
ID Continue
Ideographic
ID Start
IDS Binary Operator
IDS Trinary Operator and
Indic Mantra Category
Indic Positional Category NA
Indic Syllabic Category Other
ISO 10646 Comment
Joining Group No_Joining_Group
Join Control
Jamo Short Name
Joining Type Non Joining
Line Break Alphabetic
Logical Order Exception
Math
Noncharacter Code Point
NFC Quick Check Yes
NFD Quick Check Yes
NFKC Casefold Glyph for U+0068 Latin Small Letter H
NFKC Quick Check No
NFKD Quick Check No
Numeric Type None
Numeric Value not a number
Other Alphabetic
Other Default Ignorable Code Point
Other Grapheme Extend
Other ID Continue
Other ID Start
Other Lowercase
Other Math
Other Uppercase
Pattern Syntax
Pattern White Space
Prepended Concatenation Mark
Quotation Mark
Radical
Regional Indicator
Sentence Break Upper
Simple Case Folding Glyph for U+210D Double-Struck Capital H
Script Extension
Soft Dotted
Sentence Terminal
Terminal Punctuation
Unified Ideograph
Vertical Orientation R
Variation Selector
Word Break Alphabetic Letter
White Space
XID Continue
XID Start
Expands On NFC
Expands On NFD
Expands On NFKC
Expands On NFKD