Linear space

Japanese: 線形空間 - せんけいくうかん

〘Noun〙 In mathematics, if K is a field and V is a set, then addition is defined between elements of V, and multiplication is defined between elements of K and elements of V, and the following seven conditions are satisfied, then V is said to be a linear space over a field K (where a, b, and c are elements of V, α and β are elements of K, and 1 is the identity element of K). a+b=b+a (a+b)+c=a+(b+c) For any a and b, there exists a unique element x of V such that a+x=b. 1・a=a α(βa)=(αβ)a α(a+b)=αa+αb (α+β)a=αa+βa In this case, the elements of V are called vectors and the elements of K are called scalars. Vector space.

Source: The Selected Edition of the Japanese Language Dictionary About the Selected Edition of the Japanese Language Dictionary Information

Japanese:

〘名〙数学で、Ｋが体、Ｖが集合のとき、Ｖの元の間に加法が、Ｋの元とＶの元との間に乗法が定義されていて、次の七つの条件が満たされるならば、Ｖは体Ｋの上の線形空間であるという（ただし、ａ、ｂ、ｃはＶの元、α、βはＫの元、１はＫの単位元である）。a+b=b+a (a+b)+c=a+(b+c) 任意のａ、ｂに対して a+x=b であるＶの元ｘがただ一つ存在する。1・a=a α(βa)=(αβ)a α(a+b)=αa+αb (α+β)a=αa+βa このとき、Ｖの元をベクトル、Ｋの元をスカラーとよぶ。ベクトル空間。

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