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# U+2297Circled Times

U+2297 was added in Unicode version 1.1 in 1993. It belongs to the block U+2200 to U+22FF Mathematical Operators in the U+0000 to U+FFFF Basic Multilingual Plane.

This character is a Math Symbol and is commonly used, that is, in no specific script. The character is also known as tensor product and vector pointing into page.

The glyph is not a composition. It has no designated width in East Asian texts. In bidirectional text it acts as Other Neutral. When changing direction it is not mirrored. The word that U+2297 forms with similar adjacent characters prevents a line break inside it. The glyph can be confused with one other glyph.

The CLDR project calls this character “circled times” for use in screen reading software. It assigns these additional labels, e.g. for search in emoji pickers: product, tensor.

In mathematics, the tensor product $V\otimes W$ of two vector spaces V and W (over the same field) is a vector space to which is associated a bilinear map $V×W\to V\otimes W$ that maps a pair to an element of $V\otimes W$ denoted $v\otimes w.$

An element of the form $v\otimes w$ is called the tensor product of v and w. An element of $V\otimes W$ is a tensor, and the tensor product of two vectors is sometimes called an elementary tensor or a decomposable tensor. The elementary tensors span $V\otimes W$ in the sense that every element of $V\otimes W$ is a sum of elementary tensors. If bases are given for V and W, a basis of $V\otimes W$ is formed by all tensor products of a basis element of V and a basis element of W.

The tensor product of two vector spaces captures the properties of all bilinear maps in the sense that a bilinear map from $V×W$ into another vector space Z factors uniquely through a linear map $V\otimes W\to Z$ (see Universal property).

Tensor products are used in many application areas, including physics and engineering. For example, in general relativity, the gravitational field is described through the metric tensor, which is a vector field of tensors, one at each point of the space-time manifold, and each belonging to the tensor product with itself of the cotangent space at the point.

## Representations

System Representation
8855
UTF-8 E2 8A 97
UTF-16 22 97
UTF-32 00 00 22 97
URL-Quoted %E2%8A%97
HTML hex reference &#x2297;
Wrong windows-1252 Mojibake âŠ—
HTML named entity &CircleTimes;
HTML named entity &otimes;
alias tensor product
alias vector pointing into page
LATEX \otimes

## Complete Record

Property Value
Age (age) 1.1 (1993)
Unicode Name (na) CIRCLED TIMES
Unicode 1 Name (na1)
Block (blk) Mathematical Operators
General Category (gc) Math Symbol
Script (sc) Common
Bidirectional Category (bc) Other Neutral
Combining Class (ccc) Not Reordered
Decomposition Type (dt) none
Decomposition Mapping (dm) Circled Times
Lowercase (Lower)
Simple Lowercase Mapping (slc) Circled Times
Lowercase Mapping (lc) Circled Times
Uppercase (Upper)
Simple Uppercase Mapping (suc) Circled Times
Uppercase Mapping (uc) Circled Times
Simple Titlecase Mapping (stc) Circled Times
Titlecase Mapping (tc) Circled Times
Case Folding (cf) Circled Times
ASCII Hex Digit (AHex)
Alphabetic (Alpha)
Bidi Control (Bidi_C)
Bidi Mirrored (Bidi_M)
Composition Exclusion (CE)
Case Ignorable (CI)
Changes When Casefolded (CWCF)
Changes When Casemapped (CWCM)
Changes When NFKC Casefolded (CWKCF)
Changes When Lowercased (CWL)
Changes When Titlecased (CWT)
Changes When Uppercased (CWU)
Cased (Cased)
Full Composition Exclusion (Comp_Ex)
Default Ignorable Code Point (DI)
Dash (Dash)
Deprecated (Dep)
Diacritic (Dia)
Emoji Modifier Base (EBase)
Emoji Component (EComp)
Emoji Modifier (EMod)
Emoji Presentation (EPres)
Emoji (Emoji)
Extender (Ext)
Extended Pictographic (ExtPict)
FC NFKC Closure (FC_NFKC) Circled Times
Grapheme Cluster Break (GCB) Any
Grapheme Base (Gr_Base)
Grapheme Extend (Gr_Ext)
Hex Digit (Hex)
Hyphen (Hyphen)
ID Continue (IDC)
ID Start (IDS)
IDS Binary Operator (IDSB)
IDS Trinary Operator and (IDST)
IDSU (IDSU) 0
ID_Compat_Math_Continue (ID_Compat_Math_Continue) 0
ID_Compat_Math_Start (ID_Compat_Math_Start) 0
Ideographic (Ideo)
InCB (InCB) None
Indic Mantra Category (InMC)
Indic Positional Category (InPC) NA
Indic Syllabic Category (InSC) Other
Jamo Short Name (JSN)
Join Control (Join_C)
Logical Order Exception (LOE)
Math (Math)
Noncharacter Code Point (NChar)
NFC Quick Check (NFC_QC) Yes
NFD Quick Check (NFD_QC) Yes
NFKC Casefold (NFKC_CF) Circled Times
NFKC Quick Check (NFKC_QC) Yes
NFKC_SCF (NFKC_SCF) Circled Times
NFKD Quick Check (NFKD_QC) Yes
Other Alphabetic (OAlpha)
Other Default Ignorable Code Point (ODI)
Other Grapheme Extend (OGr_Ext)
Other ID Continue (OIDC)
Other ID Start (OIDS)
Other Lowercase (OLower)
Other Math (OMath)
Other Uppercase (OUpper)
Prepended Concatenation Mark (PCM)
Pattern Syntax (Pat_Syn)
Pattern White Space (Pat_WS)
Quotation Mark (QMark)
Regional Indicator (RI)
Sentence Break (SB) Other
Soft Dotted (SD)
Sentence Terminal (STerm)
Terminal Punctuation (Term)
Unified Ideograph (UIdeo)
Variation Selector (VS)
Word Break (WB) Other
White Space (WSpace)
XID Continue (XIDC)
XID Start (XIDS)
Expands On NFC (XO_NFC)
Expands On NFD (XO_NFD)
Expands On NFKC (XO_NFKC)
Expands On NFKD (XO_NFKD)
Bidi Paired Bracket (bpb) Circled Times
Bidi Paired Bracket Type (bpt) None
East Asian Width (ea) neutral
Hangul Syllable Type (hst) Not Applicable
ISO 10646 Comment (isc)
Joining Group (jg) No_Joining_Group
Joining Type (jt) Non Joining
Line Break (lb) Alphabetic
Numeric Type (nt) none
Numeric Value (nv) not a number
Simple Case Folding (scf) Circled Times
Script Extension (scx)
Vertical Orientation (vo) R