Element-wise arithmetic
NumPy operations between equal-size arrays apply the operation element-wise — this is what the book calls "vectorization," and it's what lets you skip writing for loops.
import numpy as np
a = np.array([1, 2, 3])
b = np.array([10, 20, 30])
print(a + b)
print(a - b)
print(a * b)
print(a / b)Scalar operations
Arithmetic with a scalar propagates that value to every element in the array (this is broadcasting in its simplest form).
import numpy as np
arr = np.array([1, 2, 3])
print(arr * 10)
print(arr + 0.5)Power and modulo
import numpy as np
arr = np.array([2, 3, 4])
print(arr ** 2) # [4 9 16]
print(arr % 2) # [0 1 0]Comparisons
Comparisons produce boolean arrays, applied element-wise just like arithmetic.
import numpy as np
arr = np.array([10, 20, 30])
print(arr > 15) # [False True True]
print(arr == 20) # [False True False]flowchart LR A["Two equal-shape arrays"] --> B["Arithmetic (+ - * /)
-> same-shape array"] A --> C["Comparison (> == <)
-> boolean array"] A --> D["Aggregation (.sum/.mean)
-> scalar or lower-dim array"] E["Two 2D arrays"] --> F["Matrix multiply (@)
-> new matrix, NOT element-wise"]
Aggregations (sum, mean, min, max)
import numpy as np
mat = np.array([
[1, 2, 3],
[4, 5, 6]
])
print(mat.sum()) # sum of all
print(mat.sum(axis=0)) # column sums
print(mat.sum(axis=1)) # row sums
print(mat.mean(axis=0))
print(mat.min(axis=1))
print(mat.max(axis=1))Matrix multiplication vs element-wise multiplication
Element-wise multiplication
* multiplies matching positions — it is not the same as matrix multiplication.
import numpy as np
a = np.array([[1, 2], [3, 4]])
b = np.array([[10, 20], [30, 40]])
print(a * b)Matrix multiplication
Use @ operator or np.matmul.
import numpy as np
a = np.array([[1, 2], [3, 4]])
b = np.array([[10, 20], [30, 40]])
print(a @ b)Rounding
import numpy as np
arr = np.array([1.234, 5.678])
print(np.round(arr, 2))
print(np.floor(arr))
print(np.ceil(arr))Check your understanding
For mat = np.array([[1, 2, 3], [4, 5, 6]]), what does mat.sum(axis=0) return?
axis=0 collapses the rows and gives one sum per column: 1+4, 2+5 and 3+6. axis=1 would give the row sums [6 15].
Show answer
B — [5 7 9] — axis=0 collapses the rows and gives one sum per column: 1+4, 2+5 and 3+6. axis=1 would give the row sums [6 15].
For a = np.array([[1, 2], [3, 4]]) and b = np.array([[10, 20], [30, 40]]), what is a * b?
The * operator multiplies matching positions: 1*10, 2*20, 3*30 and 4*40. The matrix product a @ b would be [[70 100] [150 220]].
Show answer
B — [[10 40] [90 160]] — The * operator multiplies matching positions: 1*10, 2*20, 3*30 and 4*40. The matrix product a @ b would be [[70 100] [150 220]].
What does arr % 2 return for arr = np.array([2, 3, 4])?
% is the element-wise remainder after dividing by 2. The squares [4 9 16] come from arr ** 2.
Show answer
A — [0 1 0] — % is the element-wise remainder after dividing by 2. The squares [4 9 16] come from arr ** 2.
For arr = np.array([1.234, 5.678]), which call returns [1. 6.]-style whole numbers rounded up?
np.ceil rounds every value up, giving 2 and 6. np.floor rounds down to 1 and 5, and np.round(arr, 2) keeps two decimals.
Show answer
C — np.ceil(arr) — np.ceil rounds every value up, giving 2 and 6. np.floor rounds down to 1 and 5, and np.round(arr, 2) keeps two decimals.
Next
Continue to: NumPy Universal Functions (ufuncs) to learn fast built-in vectorized functions.
🧪 Try It Yourself
Exercise 1 – Element-wise vs Matrix Multiplication
Tab indents. Press Escape, then Tab, to leave the editor. Control plus Enter runs the code; Control plus Shift plus Enter submits it.
Press Run to see what your code prints.Exercise 2 – Sum Along an Axis
Tab indents. Press Escape, then Tab, to leave the editor. Control plus Enter runs the code; Control plus Shift plus Enter submits it.
Press Run to see what your code prints.Exercise 3 – Round, Floor, Ceil
Tab indents. Press Escape, then Tab, to leave the editor. Control plus Enter runs the code; Control plus Shift plus Enter submits it.
Press Run to see what your code prints.