Matrices, Eigenvalues, and Vector Spaces

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Algebra - Linear Algebra

user_kumartyv Created by 9 mon ago

Cards in this deck(27)

null space contains only the 0 vector full rank/pivots

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columns indep

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rank = rows

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Square Det=/=0 columns indep. rows indep. full rank no zero eigenvalues Bijective

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being invertible

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n eigenvectors geom mult. of eigenvalues = alg. mult

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A = PDP⁻¹.

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The eigenvectors

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The eigenvalues on a diagonal

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diagonalizable

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Eigenvalues are on the diagonal

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product of eigenvalues

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1

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multiply of the diagonal values

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lin dep row. 0 matrix

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det(A)

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minimizes ||Ax - b||^2 Can be used for projection

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ATAx = ATb Ax is the projection of b on col(A)

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projw x

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wj dot wi= 0

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v1=w1 v2=w2-projv1w2 v3=w3-projv1w3-projv2w3

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from 2d points make A= [1 x1 1 x2] and b=[y1, y2] and check Ax=b if inconsistent check ATAx=ATb

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no

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Span of the rows as columns

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RREF and take non-zero rows or col(A^T)

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rank(A^T)

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Properties of Similar Matrices

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