what is kernel, rank and null of a matrix?
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Kinda hard to ELi5, linalg is kinda one of those things that only makes sense when you have a mostly complete picture of it, also math loves its rigorous definitions.
A matrix describes a transformation of a vector.
The set of *all vectors* that can be transformed by that matrix (called a *vector space*) is said to be *spanned* by that matrix – also called the span of the matrix
The *rank* of a matrix is a integer number that describes the dimensionality of the vector space spanned by that matrix. Or over-simply, the smallest amount of numbers that can describe a point in this space (thinking with spacial dimensions)
The *kernel* of a matrix is the set of all vectors in the span of that matrix (a subspace) that the matrix maps to the *zero vector*, (eg. (0,0) ) in other words, the set of all vectors that – when transformed by the transformation the matrix describes – become all 0’s.
The kernel is also called the *null space*.
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