math线性代数
联系向量、线性变换与矩阵计算，从几何和代数两个角度探索。
顺着知识，继续探索
线性变换
线性变换保持向量加法与数乘，其矩阵表示取决于所选的基。
从不同角度理解
非方阵：不同维度之间的线性变换｜3Blue1Brown
3Blue1Brown · en · 讲解关联依据
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。
非方阵：不同维度之间的线性变换｜3Blue1Brown
3Blue1Brown · en · 讲解关联依据
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.