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  • Linear independency before and after Linear Transformation
    Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
  • linear algebra - What is the difference between linearly and affinely . . .
    Intuitively, a set of vectors is linearly dependent if there are more vectors than necessary to generate their span, i e the smallest subspace containing them On the other hand, a set of vectors is affinely dependent if there are more vectors than necessary to generate their affine hull, i e the smallest flat (translate of a linear space
  • linear algebra - Determine if vectors are linearly independent . . .
    Because we know that if $\det M \neq 0$, the given vectors are linearly independent (However, this method applies only when the number of vectors is equal to the dimension of the Euclidean space ) (However, this method applies only when the number of vectors is equal to the dimension of the Euclidean space )
  • How to Tell If Matrices Are Linearly Independent
    Another alternative for testing is to check for the determinant for each matrices (this may look tedious for a complicated matrix system), If the determinant is non zero, It is said to be Linearly Independent, and if the determinant is zero, it is Linearly dependent
  • definition - Is a linear combination linearly independent . . .
    The vectors are linearly independent if the only linear combination of them that's zero is the one with all $\alpha_i$ equal to 0 It doesn't make sense to ask if a linear combination of a set of vectors (which is just a single vector) is linearly independent Linear independence is a property of a set of vectors
  • What exactly does linear dependence and linear independence imply . . .
    Let S be the set of vectors S = {V1, V2, V3,… ,Vn} The set S is linearly dependent if and only if CV1+ C2V2 + C3V3 +… + CnVn=zero vector for some all Ci’s at least one is non zero The condition of checking linear dependence if c1 or c2 is non zero then the two vectors are linearly dependent Linearly Independence
  • What does it mean when we say a variable changes linearly?
    I have attached a screenshot in which a variable is defined for an object somehow that it linearly decreases from 500 micrometers at the top of the object to 50 micrometers at the bottom of the object I was wondering what does it mean by linearly decreases?
  • linear independent rows of a matrix - Mathematics Stack Exchange
    Linearly independent means that every row column cannot be represented by the other rows columns Hence it is independent in the matrix Hence it is independent in the matrix When you convert to row reduced echelon form , we look for "pivots"
  • Determinant of a matrix and linear independence (explanation needed)
    The n vectors are linearly dependent iff the zero vector is a nontrivial linear combination of the vectors (definition of linearly independent) The zero vector is a nontrivial linear combination of the vectors iff the matrix times some nonzero vector is zero (definition of matrix multiplication)





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