Vector Space

Description

Mind Map so that we could see a bigger picture of vector space
Sweetie Happy
Mind Map by Sweetie Happy, updated more than 1 year ago
Sweetie Happy
Created by Sweetie Happy over 6 years ago
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Resource summary

Vector Space
  1. Linear Independence
    1. Linear Span
      1. Ax=b
        1. Vector Subspace
          1. Finite Dimensional Spaces
            1. Basis / Base
              1. Ordered, spanning set of linear independent vectors.
                1. Change Base
          2. Square Matrix
            1. - Inverse of A exists.
              1. Determinant is non zero
                1. Rows of A are linearly independent.
                  1. x zero row after row reduction
                    1. rank(A) + nullity(A) = dim-dom A
                      1. Kernel(T) = Null Space
                        1. T(u) = 0
                        2. Range Space = Image Space
                          1. T(u) =v
                          2. scalar
                          3. Linear Transformations
                            1. Eg. Matrix Transformation
                              1. Inner Product Space
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