Intermediate

Shape Manipulation & Broadcasting

Reshaping, stacking, and the rule that lets mismatched shapes still add.

reshape relabels the same flat data into a new shape; it does not reorder data the way a transpose does. If you find yourself needing rows to become columns, that's .T / np.transpose, not reshape.

Broadcasting is how NumPy applies an operation to two arrays of different shapes without you writing a loop. Compare shapes from the right; two dimensions are compatible if they're equal, or one of them is 1 (it gets "stretched" to match). Play with the examples below.

Function	Effect	Example
`np.concatenate([a, b], axis=0)`	join along an existing axis	`concatenate([[1,2],[3,4]])` → `[1, 2, 3, 4]` (1-D arrays)
`np.vstack([a, b])`	stack as rows	`vstack([[1,2],[3,4]])` → `[[1,2],[3,4]]` (2 rows)
`np.hstack([a, b])`	stack side by side	`hstack([[1,2],[3,4]])` → `[1,2,3,4]`
`np.stack([a, b], axis=0)`	join along a brand-new axis	`stack([[1,2],[3,4]])` → shape `(2, 2)`, a new leading axis
`a.squeeze()`	drop all size-1 dimensions	shape `(1, 3, 1)` → `(3,)`
`np.expand_dims(a, axis=0)`	insert a new size-1 dimension	shape `(3,)` → `(1, 3)`

Now practice it

Exercises that use what this lesson just covered.

3×3 Matrix 0–8Easy Checkerboard PatternEasy Matrix ProductEasy Stack Two Vectors as RowsEasy Concatenate Two Vectors End-to-EndEasy Stack Two Matrices Along a New AxisMedium

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