Summary: Matrices, Graphs And Convexity
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Read the summary and the most important questions on Matrices, Graphs and Convexity
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1 Introduction Matrices
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1.1 Matrices and linear maps
This is a preview. There are 6 more flashcards available for chapter 1.1
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In C=AB, then cij is horizontal times vertical or the other way around?
Sumproduct of horizontal times vertical -
What is the characteristic of a permutation matrix?
Every row and every column has all zero entries except for one entry which is 1. -
What is another term for regular? (matrices)
non-singular -
If det(A) ≠ 0, what holds about the singularity?
det(A) ≠ 0 ⇔ A is regular (non-singular) -
What is the intuition behind a surjective map?
That x maps to y, that is, all values in the set of possible outcomes can be reached from the domain. -
What two conditions must hold in order to call map f linear?
1. f(x+y) = f(x) + f(y)
2. f(δx) = δ f(x) -
For every linear map there exists a matrix which resembles that mapping; what property of that matrix says something about the bijectiveness of the mapping?
The map f is bijective if and only if the corresponding matrix is regular -
What is the kernel of a matrix A?
All values that multiplied by A result in all zeros -
What is the image of A?
The collection of all possible resulting vectors of multiplication by A -
1.2 Special matrices
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When is matrix A positive definite? (mathematical)
xTAx > 0 for all x∈Rn\{0}
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