Matrix Rank - PowerPoint PPT Presentation

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Matrix Rank

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Evaluation of rank of a matrix – PowerPoint PPT presentation

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Title: Matrix Rank


1
Matrix Rank
  • Rank Definition
  • Rank Computation
  • Rank Properties
  • Rank and Linear System AXB

2
Rank Definition
  • Column Rank
  • is the maximum number of linearly independent
    column vectors in A
  • Row Rank
  • is the maximum number of linearly independent row
    vectors in A
  • Theorem Column Rank Row Rank

3
Rank Computation
  • Ex. Find Rank(A) where
  • By applying Gauss-Elimination
  • Rank(A)2 (number of non-zero rows after
    Gauss-Elimination)
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