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Matrices

concept
  • Requires → Vectors
    EvidenceEditorial suggested sequence; verify the course context. [linear-algebra]
  • Leads to → Linear systems
    EvidenceEditorial suggested sequence; verify the course context. [linear-algebra]
  • Leads to → Rank and nullity
    EvidenceEditorial suggested sequence; verify the course context. [linear-algebra]
  • Leads to → Determinants
    EvidenceEditorial suggested sequence; verify the course context. [linear-algebra]
  • Leads to → Linear transformations
    EvidenceEditorial suggested sequence; verify the course context. [linear-algebra]
  • Explanation → Matrices
    EvidenceCandidate 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。
  • Explanation → Matrices
    EvidenceCandidate 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。
  • Explanation → Matrices
    EvidenceCandidate from reviewed en material v1: This example uses square matrices of order 2. A matrix organizes its entries into horizontal rows and vertical columns.
  • Explanation → Matrices
    EvidenceCandidate 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.
  • Explanation → Matrices
    EvidenceCandidate 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.
  • Explanation → Matrices
    EvidenceCandidate from reviewed zh material v1: 本例使用2阶方阵;矩阵的元素按横行与竖列组织。

Vectors

concept
  • Leads to → Matrices
    EvidenceEditorial suggested sequence; verify the course context. [linear-algebra]

Linear systems

concept
  • Requires → Matrices
    EvidenceEditorial suggested sequence; verify the course context. [linear-algebra]

Rank and nullity

concept
  • Requires → Matrices
    EvidenceEditorial suggested sequence; verify the course context. [linear-algebra]

Determinants

concept
  • Requires → Matrices
    EvidenceEditorial suggested sequence; verify the course context. [linear-algebra]

Matrix addition and subtraction | Matrices | Precalculus | Khan Academy

video
  • Content location → Matrices
    EvidenceCandidate 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。
  • Content location → Matrices
    EvidenceCandidate 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.

Matrices

segment
  • Content location → Matrix addition and subtraction | Matrices | Precalculus | Khan Academy
    EvidenceCandidate 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。
  • Explanation → Matrices
    EvidenceCandidate 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

video
  • Content location → Matrices
    EvidenceCandidate 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。
  • Content location → Matrices
    EvidenceCandidate 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.

Matrices

segment
  • Content location → Nonsquare matrices as transformations between dimensions | 3Blue1Brown
    EvidenceCandidate 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。
  • Explanation → Matrices
    EvidenceCandidate 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。

Worked example: matrix multiplication associativity

video
  • Content location → Matrices
    EvidenceCandidate from reviewed en material v1: This example uses square matrices of order 2. A matrix organizes its entries into horizontal rows and vertical columns.
  • Content location → Matrices
    EvidenceCandidate from reviewed zh material v1: 本例使用2阶方阵;矩阵的元素按横行与竖列组织。

Matrices

segment
  • Content location → Worked example: matrix multiplication associativity
    EvidenceCandidate from reviewed en material v1: This example uses square matrices of order 2. A matrix organizes its entries into horizontal rows and vertical columns.
  • Explanation → Matrices
    EvidenceCandidate from reviewed en material v1: This example uses square matrices of order 2. A matrix organizes its entries into horizontal rows and vertical columns.

Matrices

segment
  • Content location → Matrix addition and subtraction | Matrices | Precalculus | Khan Academy
    EvidenceCandidate 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.
  • Explanation → Matrices
    EvidenceCandidate 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.

Matrices

segment
  • Content location → Nonsquare matrices as transformations between dimensions | 3Blue1Brown
    EvidenceCandidate 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.
  • Explanation → Matrices
    EvidenceCandidate 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.

Matrices

segment
  • Content location → Worked example: matrix multiplication associativity
    EvidenceCandidate from reviewed zh material v1: 本例使用2阶方阵;矩阵的元素按横行与竖列组织。
  • Explanation → Matrices
    EvidenceCandidate from reviewed zh material v1: 本例使用2阶方阵;矩阵的元素按横行与竖列组织。