INVERTIBLE Meaning and
Definition
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In mathematics, the term "invertible" is used to describe a mathematical object, such as a function or matrix, that has an inverse. An inverse is a counterpart that undoes or reverses the effect of the original object, bringing it back to its original state.
For example, in the context of functions, an invertible function is a function where each element of the domain corresponds to exactly one element in the range, and vice versa. This implies that given an output value, we can uniquely determine the input value that produced it. In other words, we can "reverse" the function to obtain the original input.
Similarly, in linear algebra, an invertible matrix is a square matrix that has an inverse matrix. The inverse matrix, when multiplied with the original matrix, produces the identity matrix. This means that the original matrix can be "reversed" by multiplying it by its inverse.
In general, for an object to be invertible, it has to satisfy certain conditions. For functions, this often involves being one-to-one (injective) and onto (surjective), ensuring that every input value has a unique output value, and vice versa. In the case of matrices, invertibility is typically connected to the concept of determinant, where a non-zero determinant signifies invertibility.
Common Misspellings for INVERTIBLE
Etymology of INVERTIBLE
The word "invertible" derives from the Latin word "invertere", which consists of two parts: "in" meaning "in" or "into", and "vertere" meaning "to turn" or "to change". These Latin roots convey the idea of "turning inwards" or "changing the order" of something. When applied to mathematics or other disciplines, "invertible" refers to a function or element that can be reversed or undone, implying that it can be turned back into its original state or order.
Similar spelling words for INVERTIBLE
- inevitably,
- inoperable,
- inebriated,
- inebriant,
- inebriate,
- unaffordable,
- inverse,
- convertible,
- Unfordable,
- unaffordably,
- inversely,
- non-invertible,
- infertile,
- inedible,
- inebriety,
- inverted hang,
- invertase,
- unavertable,
- inoperative,
- inverted,
- inverter,
- invertebrate,
- inevitable,
- unavertible.
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