前置知识 → 向量空间依据Editorial suggested sequence; verify the course context. [linear-algebra]
前置知识 → 矩阵依据Editorial suggested sequence; verify the course context. [linear-algebra]
后续学习 → 特征值与特征向量依据Editorial suggested sequence; verify the course context. [linear-algebra]
讲解 → 线性变换依据Candidate from reviewed zh material v1: 分屏示意图把三维输入映到二维平面。三个基向量像的箭头说明如何确定这种跨维映射；箭头位置不应当被视为前面数值矩阵的计算结果。
讲解 → 非方阵：不同维度之间的线性变换｜3Blue1Brown依据Candidate from reviewed en material v1: A nonsquare matrix represents a linear map between coordinate spaces with different dimensions. Count its columns to find the input dimension and its rows to find the output dimension. The lesson constructs a 3×2 matrix from two basis images, interprets its column space as a plane in three-dimensional space, and explains full column rank in that example. It then contrasts 2×3 and 1×2 maps and reads the row matrix [1,2] from basis vectors landing on the number line. Separate dimensional diagrams are illustrations rather than computations with one shared matrix. Dot products and duality appear as a closing preview.
内容位置 → 线性变换依据Candidate from reviewed zh material v1: 分屏示意图把三维输入映到二维平面。三个基向量像的箭头说明如何确定这种跨维映射；箭头位置不应当被视为前面数值矩阵的计算结果。
讲解 → 线性变换依据Candidate from reviewed en material v1: A nonsquare matrix represents a linear map between coordinate spaces with different dimensions. Count its columns to find the input dimension and its rows to find the output dimension. The lesson constructs a 3×2 matrix from two basis images, interprets its column space as a plane in three-dimensional space, and explains full column rank in that example. It then contrasts 2×3 and 1×2 maps and reads the row matrix [1,2] from basis vectors landing on the number line. Separate dimensional diagrams are illustrations rather than computations with one shared matrix. Dot products and duality appear as a closing preview.
math