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Matrices

A matrix is a rectangular array representing data or a linear map in chosen bases; matrix multiplication represents composition when dimensions agree.

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Different ways to understand it

• Matrix addition and subtraction | Matrices | Precalculus | Khan Academy

  Khan Academy · en · Explanation
  Connection evidence

  Candidate from reviewed zh material v1: 矩阵加法按对应位置定义。两个矩阵必须具有相同的行数和列数；结果保留这个形状，每个元素等于两个输入在对应位置上的元素之和。

• Nonsquare matrices as transformations between dimensions | 3Blue1Brown

  3Blue1Brown · en · Explanation
  Connection evidence

  Candidate from reviewed zh material v1: 3×2 矩阵表示从二维输入空间到三维输出空间的线性映射。其非方形状记录了不同数量的输入和输出坐标。

• Matrix addition and subtraction | Matrices | Precalculus | Khan Academy

  Khan Academy · en · Explanation
  Connection evidence

  Candidate from reviewed en material v1: The instructor writes capital letters A and B above the two matrices. These labels express the comparison as A+B=B+A.

• Nonsquare matrices as transformations between dimensions | 3Blue1Brown

  3Blue1Brown · en · Explanation
  Connection evidence

  Candidate from reviewed en material v1: A linear map with input and output spaces of the same dimension has a square matrix representation once bases are chosen. The earlier examples use 2×2 and 3×3 matrices.

Knowledge connections

• Vectors · Prerequisite · Map context
• Linear systems · Next concept · Map context
• Rank and nullity · Next concept · Map context
• Determinants · Next concept · Map context
• Linear transformations · Next concept · Map context

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