Why Matrix Multiplication Uses new_pixel[row][0] When Processing RGB Pixels

[Rajeev Bagra]

Q&A: Understanding [row][0] in Matrix-Based Pixel Transformation

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Context

You are implementing a color-filter function that simulates color-vision deficiency.
Each pixel is transformed using matrix multiplication.

Relevant code snippet

for r, g, b in pixels_list:
    pixel_vector = [[r], [g], [b]]
    new_pixel = matrix_multiply(transform, pixel_vector)

    result.append((
        max(0, min(255, int(new_pixel[0][0]))),
        max(0, min(255, int(new_pixel[1][0]))),
        max(0, min(255, int(new_pixel[2][0])))
    ))

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Question

Why do we use new_pixel[0][0], new_pixel[1][0], and new_pixel[2][0]?
Why is the second index always 0 for all three color values?

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Answer

1. What matrix_multiply returns

The multiplication:

matrix_multiply(transform, pixel_vector)

multiplies a 3×3 matrix by a 3×1 column vector.

So the result is a 3×1 matrix, not a flat list.

Its structure is:

new_pixel = [
    [new_r],
    [new_g],
    [new_b]
]

Each color value is stored inside its own list.

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2. Meaning of the indices

First index → row (which color)

new_pixel[0] → [new_r]
new_pixel[1] → [new_g]
new_pixel[2] → [new_b]

Second index → column

Each row has only one column, so the column index is always 0.

new_pixel[0][0] → new_r
new_pixel[1][0] → new_g
new_pixel[2][0] → new_b

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3. Why the second index cannot be anything else

This is a column vector:

3 rows × 1 column

There is no column 1 or 2, only column 0.

Trying new_pixel[0][1] would cause an error.

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4. Why not return a flat list?

Matrix math conventions require:

• Matrices and vectors to be represented as 2D structures
• Consistent shapes for multiplication

Returning a column vector keeps the math correct and predictable.

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One-line takeaway

The second [0] exists because the matrix multiplication result is a 3×1 column vector, and each color value lives in column zero of its row.

This is a data-structure rule, not a color-processing trick.

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