math 141 all definitions

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61 Terms

1
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LU Gaussian

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2
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Upper Echelon

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Pivot

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Rank

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Augmented Matrix

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Matrix vector equation

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Back Substitution

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Vector Addition

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Scalar Multiplication

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10
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Linear Combination

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Column Picture

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12
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Row Picture

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13
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Span

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Subspace

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15
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Linear Independence

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Trivial Solution

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17
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Basis

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18
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Dimensiobn

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Homogenous System

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Nullspace

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21
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Column Space

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Transpose

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Row Space

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Left Nullspace

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Complete Solution

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26
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Identity Matrix

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27
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Linear Transformation

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28
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Kernal

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29
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Range

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Injective

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Surjective

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Bijective

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Dor (or inner) product

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Norm

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Orthogonal Projection

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Projection

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37
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Inverse of a linear transformation

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38
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Inverse Matrix

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Gauss-Jordan method to compute in inverse matrices

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40
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Determinant (computational)

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Determinant (volume)

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42
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Determinant (linear transformation)

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Orthogonal subspaces

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Orthogonal complement

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45
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Schwarz Inequality

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Triangle inequality

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Projection matrix

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48
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Orthonormal

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49
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Orthogonal matrix

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50
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Gram-Schmidt

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51
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Eigenvalue / Eigenvector

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Eigenspace

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53
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Algebraic Multiplicity

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Geometric Multiplicity

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Similar Matrices

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Diagonalization

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Change of basis matrix

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Nullspace
Left Nullspace

Fundemental Theorem of Linear Algebra (part 2)
1) The ____ is the orthogonal compliment to the rowspace in Rn
2) The ____ is the orthogonal compliment to the column space in Rn.

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Positive (semi) definite matrix

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60
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Symmetric Matrix

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Singular Value Decomposition

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