MIT 18.06 : Linear Algebra

Row PictureColumn Picture
U1V1U2V2 xy = U1*x + V1*yU2*x + V2*y U1V1U2V2 xy = x U1U2 + y V1V2
By RowsBy Columns
Row x Matrix = RowMatrix x Column = Column
xy U1U2V1V2 = x U1U2 + y V1V2 U1V1U2V2 xy = x U1U2 + y V1V2
BlockDotColumnsRowsColumn x Row
[B1][B2][B3][B4] [b1][b2][b3][b4] = [B1][b1]+[B2][b3][B1][b2]+[B2][b4][B3][b1]+[B4][b3][B3][b2]+[B4][b4] - R1 -- R2 - ||C1C2|| = - R1 - |C1| - R1 - |C2| - R2 - |C1| - R2 - |C2| M ||C1C2|| = M |C1| M |C2| -R1--R2- M = - R1 - M - R2 - M ||C1C2|| - R1 -- R2 - = Σ |Ci| - Ri -
A=LU
1327
A
1001
I
1301
EA=U
10-21
EI=E
→ L = E⁻¹ = 1021
1327
A
=
1021
L
1301
U