Linear Algebra 30 | Injectivity, Surjectivity for Square Matrices

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(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

[@drioko]

i like the background color makes me feel calmer and happier

[@brightsideofmaths]

Nice :)

[@salimallami5790]

Please, as you know the matrix multiplied by x, gives us b, is a set of linear equations. Question 1: Do we mean that the matrix is injective or surjective? Or linear equations crystallized into functions? . Question 2: For example, a matrix consists of linear equations defined as functions. One of these functions is surjective, and the other is injective, meaning it is mixed. How do we distinguish the type of matrix in light of that? Thank you very much for your wonderful effort.

[@latinadna]

difference between a well-defined and bijective map: well-defined is about clarity and consistency in the mapping process, whereas being bijective is about the specific relationships between the domain and codomain in terms of one-to-one and onto mappings. A bijective function is always well-defined, as it meets the criteria of providing a unique output for every input and covering the entire codomain. However, being well-defined is a more basic requirement than being bijective.

[@latinadna]

a function can still be well-defined even if two different inputs in the domain are mapped to the same output. as long as each input in the domain is associated with exactly one output in the codomain.

[@sibichakravarthy037]

what does injectivity mean?

[@brightsideofmaths]

You can check it here: tbsom.de/s/sls