1 
Orthogonal complements

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2 
dim(v) + dim(orthogonal complement of v) = n

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3 
Representing vectors in rn using subspace members

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4 
Orthogonal complement of the orthogonal complement

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5 
Orthogonal complement of the nullspace

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6 
Unique rowspace solution to Ax = b

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7 
Rowspace solution to Ax = b example

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8 
Projections onto subspaces

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9 
Visualizing a projection onto a plane

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10 
A projection onto a subspace is a linear transformation

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11 
Subspace projection matrix example

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12 
Another example of a projection matrix

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13 
Projection is closest vector in subspace

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14 
Least squares approximation

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15 
Least squares examples

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16 
Another least squares example

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17 
Coordinates with respect to a basis

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18 
Change of basis matrix

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19 
Invertible change of basis matrix

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20 
Transformation matrix with respect to a basis

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21 
Alternate basis transformation matrix example

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22 
Alternate basis transformation matrix example part 2

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23 
Changing coordinate systems to help find a transformation matrix

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24 
Introduction to orthonormal bases

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25 
Coordinates with respect to orthonormal bases

Linear algebra (KA)

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