zero map

DefinitionSuppose $X$ is a set, and $Y$ is a vector space with zero vector $0$ .If $Z$ is a map $Z:X\\to Y$ , such that $Z(x)=0$ for all $x$ in $X$ ,then $Z$ is a zero map.

0.0.1 Examples

1.
On the set of non-invertible $n\\times n$ matrices, the determinantis a zero map.
2.
If $X$ is the zero vector space, any linear map $T:X\\to Y$ isa zero map. In fact, $T(0)=T(0\\cdot 0)=0T(0)=0$ .
3.
If $X=Y$ and its field is $\\mathbb{R}$ or $\\mathbb{C}$ , then the spectrum of $Z$ is $\\{0\\}$ .

单词	ZeroMap
释义	zero map DefinitionSuppose $X$ is a set, and $Y$ is a vector space with zero vector $0$ .If $Z$ is a map $Z:X\\to Y$ , such that $Z(x)=0$ for all $x$ in $X$ ,then $Z$ is a zero map. 0.0.1 Examples 1. On the set of non-invertible $n\\times n$ matrices, the determinantis a zero map. 2. If $X$ is the zero vector space, any linear map $T:X\\to Y$ isa zero map. In fact, $T(0)=T(0\\cdot 0)=0T(0)=0$ . 3. If $X=Y$ and its field is $\\mathbb{R}$ or $\\mathbb{C}$ , then the spectrum of $Z$ is $\\{0\\}$ .
随便看	Halgebra H * -algebra HalleysFormula Halley’s formula HallsMarriageTheorem HallsMarriageTheoremProofOf HallSubgroup Hall subgroup Hall’s marriage theorem Hall’s marriage theorem, proof of HaltingProblem halting problem HamelFunction Hamel function HamiltonEquations Hamilton equations HamiltonianAlgebroids Hamiltonian algebroids HamiltonianCycle Hamiltonian cycle HamiltonianGraph Hamiltonian graph HamiltonianGroup Hamiltonian group HamiltonianOperator