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单词 Euclidean space
释义

Euclidean space

(Cartesian space) The number line R, plane R2, and 3‐dimensional space R3 can be generalized to n‐dimensional Euclidean or Cartesian space Rn with coordinates (x1, x2,…, xn) on which the operations of addition and scalar multiplication are extended in the obvious way. While Rn is hard to visualize for n>3, it provides a powerful framework in linear algebra and multivariable analysis.

If the points P and Q have coordinates (x1, x2,…, xn), and (y1, y2,…, yn) respectively, then the distance PQ can be defined to be equal to

Sometimes n‐dimensional Euclidean space is denoted as En, signifying that space has no predetermined coordinates, no natural origin or axes. Once an origin, perpendicular axes, and unit length have been decided, coordinates may be assigned and En can now be identified with Rn.

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更新时间:2025/5/20 18:44:15