left inverse
A 'left inverse' is a concept in mathematics that ensures a function or matrix can be reversed or undone when applied from the left side.
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Definition
C1Mathematics
(technical, academic)A function that, when composed with another function from the right, returns the original input.
Example
- If g is a left inverse of f, then applying g after f returns the original value.
C1Linear Algebra
(technical, academic)A matrix that, when multiplied from the left by another matrix, results in the identity matrix.
Example
- Matrix L is a left inverse of matrix A if L times A equals the identity matrix.
C2Abstract Algebra
(technical, academic)An element that, when combined with another element using a binary operation, results in the identity element.
Example
- In a group, an element b is a left inverse of a if b combined with a gives the identity element.
Similar
Terms that have similar or relatively close meanings to "left inverse":