Matrix Multiplication: A Nutrition Calculator

A nutrition label is a column of numbers, and eating is a matrix multiplication. Put the labels of three foods side by side to get a 3×3 matrix N: each column is one food, each row is one nutrient (grams per 100 g of that food). If a person eats amounts v_A, v_B, v_C (in units of 100 g), the total nutrients eaten are exactly the product

Nv = total grams of (carb, fat, protein), (Nv)_i = N_iAv_A + N_iBv_B + N_iCv_C

1. The nutrient matrix N — three food labels, side by side

Edit any entry (grams per 100 g of food). Column = food, row = nutrient.

Nutrient values in grams per 100 grams for Foods A, B, and C
g per 100 g	Food A	Food B	Food C
Carbohydrate
Fat
Protein

2. The amount vector v — what the person eats

Slide to choose how much of each food is eaten. The vector entry is the amount in units of 100 g.

Food A

Food B

Food C

3. The product Nv — total nutrients eaten

Hover, tap, or focus a result entry to see which numbers produced it: one row of N meets the whole vector v.

N (3×3)

v (3×1)

Nv (3×1)

4. Who contributed what? — the column picture

Each bar is one nutrient total, split by food. Hover or focus a segment for its term N_ij · v_j.

Food A Food B Food C

5. Estimated food energy from carbohydrate, fat, and protein — an inner product

Assign an energy factor (kcal/g) to each of the three nutrients. Collect these factors in a row vector c = (c_carb, c_fat, c_prot). The estimated energy represented by this model is the inner product of c with the nutrient-total vector Nv: c · (Nv) = c_carb(Nv)₁ + c_fat(Nv)₂ + c_prot(Nv)₃.

Energy factors in kilocalories per gram for the three nutrients
kcal per g	Carbohydrate	Fat	Protein
c

c (1×3)

Nv (3×1)

kcal (1×1)

The default entries 4, 9, and 4 are the Atwater factors.