Linear Algebra 30 | Injectivity, Surjectivity for Square Matrices

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This is my video series about Linear Algebra. I hope that it will help everyone who wants to learn about it.

#LinearAlgebra
#Vectors
#Matrices
#MachineLearning
#Eigenvalues
#Calculus
#Mathematics
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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)

[salimallami]

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.

[drioko]

i like the background color makes me feel calmer and happier

[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.