PART 01
行Row
这里一行保存一条商品样本向量。Here, one row stores one product sample vector.
01 · 三件商品，三个特征01 · Three products, three features
怎样把三条向量放在一起，还能一眼找到“第 2 条样本的价格”？How can three vectors stay together while “the price of sample 2” remains easy to locate?
023×3 矩阵编辑台3×3 Matrix Editor
单元格联动型Cell-linked view
行Rows
3
样本向量sample vectors
列Columns
3
特征位置feature positions
当前值Active value
2.0
Mij
03矩阵里的 4 个位置概念Four Position Concepts in a Matrix
行与列各有职责Rows and columns have rolesPART 02
列Column
这里一列收集所有样本的同一个特征。Here, one column collects the same feature across samples.
PART 03
单元格Cell
Mij 是第 i 行、第 j 列交叉处的一个标量。Mij is one scalar at row i and column j.
PART 04
形状Shape
3×3 先写行数再写列数，说明一共有 9 个位置。3×3 lists rows before columns and contains nine positions.
04最小机制：用两个索引找到一个标量Minimal Mechanism: Two Indices Find One Scalar
Mij
M ∈ R3×3, Mij = row i ∩ column j
在上方点任一输入框：高亮行确定哪条样本，高亮列确定哪个特征，交叉点就是当前值。Focus any input above: the highlighted row selects a sample, the
column selects a feature, and their intersection is the
value.
选择行 iChoose row i定位一条向量Locate one vector
选择列 jChoose column j定位同一特征Locate one feature
读取 MijRead Mij得到一个标量Get one scalar
05边界实验：让第二行少一个格Boundary Test: Remove One Cell from Row Two
主动制造失败Create a failure制造不齐整的“矩阵”Create a ragged “matrix”
点击后删掉第 2 条样本的价格。第二行只剩两个位置，列就无法保持同一含义。Remove price from sample 2. Its row now has two positions and the columns no longer preserve one shared meaning.
尚未执行。矩阵必须保持每行同样多的列。Not run yet. Every matrix row must keep the same number of
columns.
✗ 一行可以随意多一个或少一个值。A row may freely contain more or fewer
values.
→ ✓ 矩阵是矩形，每行列数必须一致。A matrix is rectangular; every row has equal
length.
✗ 3×5 表示 3 列、5 行。3×5 means three columns and five rows.
→ ✓ 形状约定先行后列。Shape notation lists rows before columns.
✗ 行列只是排版，没有含义。Rows and columns are only visual layout.
→ ✓ 索引含义决定数值如何被解释和计算。Index roles determine interpretation and
computation.
06 · 一句话带走06 · One line to keep