NumPy Translation: From Concept to Code

This page is a guide for translating linear algebra concepts into executable NumPy code. Use the tool below to translate your own formulas or explore the reference guide.

Interactive Algorithm Translator

Reference Guide

Element-wise Operations (Addition, Subtraction, etc.)

For two matrices, A and B, of the same shape, these operations are applied element by element.

Linear Algebra

A + B, A - B, A ⊙ B, A ⊘ B

NumPy Code

A + B, A - B, A * B, A / B

Scalar Operations

Adding or multiplying a single number (a scalar) to a matrix applies the operation to every element.

Linear Algebra

c + A, c ⋅ A

NumPy Code

c + A, c * A

Matrix Multiplication (Dot Product)

This is true matrix multiplication, where the number of columns in the first matrix must match the number of rows in the second. Note the different operator from element-wise multiplication.

Linear Algebra

A ⋅ B

NumPy Code

A @ B # or np.dot(A, B)

Transpose

Swapping the rows and columns of a matrix.

Linear Algebra

Aᵀ

NumPy Code

A.T # or A.transpose()

Inverse

Finding the inverse of a square matrix A such that A ⋅ A⁻¹ results in the identity matrix.

Linear Algebra

A⁻¹

NumPy Code

np.linalg.inv(A)

Determinant

A scalar value that can be computed from the elements of a square matrix.

Linear Algebra

det(A) or |A|

NumPy Code

np.linalg.det(A)

Identity Matrix

A square matrix with ones on the main diagonal and zeros everywhere else.

Linear Algebra

Iₙ

NumPy Code

np.eye(n)

Summation (Across an Axis)

Summing all elements in a matrix, or summing along a specific row or column.

Linear Algebra

Σ A (total), Σ Aᵢ (rows), Σ Aⱼ (cols)

NumPy Code

A.sum(), A.sum(axis=1), A.sum(axis=0)

Why This Matters

This direct mapping is the bridge from theory to practice. It means the conceptual algorithms we co-create in MS Pilot are not just abstract ideas. Each mathematical formula in a 'summation' can be directly translated into a line of NumPy code. This allows you to take the algorithms you synthesize here and implement them directly in computational environments like Jupyter or Google Colab notebooks, turning abstract reasoning into executable analysis.