Element-wise math, matrix dot products, and value-wise comparison.

Arithmetic

• df.add() or df.__add__ → Add element-wise; supports fill_value.
• df.sub() or df.__sub__ → Subtract element-wise.
• df.mul() or df.__mul__ → Multiply element-wise.
• df.div() or df.truediv() → Divide element-wise (true division).
• df.floordiv() → Floor division.
• df.mod() → Modulo.
• df.pow() → Exponentiate.
• df.dot() → Matrix multiplication.
• df.radd(), df.rsub(), df.rmul(), df.rdiv(), df.rtruediv(), df.rfloordiv(), df.rmod(), df.rpow() → Reverse operations.

Comparison

• df.lt() → Element-wise less than.
• df.gt() → Greater than.
• df.le() → Less than or equal.
• df.ge() → Greater than or equal.
• df.eq() → Equal to.
• df.ne() → Not equal to.

Combine

• df.combine(other, func) → Combine two DataFrames element-wise using a function.
• df.combine_first(other) → Fill missing values with other.

Math, Binary Operations & Comparison in Pandas DataFrames

⚠️ Vectorization Principle

Pandas operations are designed to work on entire arrays at once. These methods leverage NumPy's vectorized operations, making them dramatically faster than Python loops.