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RSS订阅原创 Linear Algebra Lecture 11
Linear Algebra Lecture 111. Matrix space2. Bases of new vector spaces3. Rank one matricesMatrix spaceAll 3×33×33 \times 3 matrices, every 3 by 3 matrix is one of vectors. They are ve...
2018-02-22 23:42:32
344
原创 Linear Algebra Lecture 10
Linear Algebra Lecture 101. Four Fundamental SubspacesFour subspacesColumn space C(A)C(A)C(A) Null space N(A)N(A)N(A) Row space = All combinations of rows of AAA = All combinations of ATATA^...
2018-02-18 02:13:11
421
原创 Linear Algebra Lecture 9
Linear Algebra Lecture 91. Linear independence2. Spanning a space3. Basis and DimensionIndependenceVectors X1,X2,...XnX1,X2,...XnX_1,X_2,...X_n are independent if no combination gives zero...
2018-02-13 23:10:14
342
原创 Linear Algebra Lecture 8
Linear Algebra Lecture 81. Complete solution of Ax=b" role="presentation">Ax=bAx=bAx=b2. Rank rExample 1{x1+2x2+2x3+2x4=b12x1+4x2+6x3+8x4=b23x1+6x2+8x3+10x4=b3" role="presentation">⎧⎩⎨x1+2x2
2018-02-07 01:26:03
384
原创 Linear Algebra Lecture 7
Linear Algebra Lecture 71. Computing the nullspace2. Pivot variables and free variables3. Special solutions4. rref(A) = RExample 1Compution the nullspace for a matrix A, find all the sol
2018-02-02 23:59:42
318
原创 Linear Algebra Lecture 6
Linear Algebra Lecture 61.Vector spaces and subspaces2. Column space of A3. Null space of AVector spaceVector space requirements v+wv+w and cvcv are in the space, all the linear combinat
2018-01-22 22:50:06
293
原创 Linear Algebra Lecture 5
Linear Algebra Lecture 51. Permutations PA=LUPA=LU2. Vector spaces and subspacesPermutationsThey execute row exchanges. P is the identity matrix with reordered rows. PA=LUPA=LU This is
2018-01-21 23:52:19
370
原创 Linear Algebra Lecture 4
Linear Algebra Lecture 41.Inverse of ABAB, ATA^T2.Product of elimination matrices A=LUA=LU3.PermutationsWhat’s the Inverse of AB?Suppose A is invertible and B is invertible, what matrix
2018-01-18 00:11:44
273
原创 Linear Algebra Lecture 3
Linear Algebra Lecture 31.Matrix multiplication in 4 ways2.Inverse of A, AB, ATA^T3.Gauss-Jordan ideaMatrix multiplicationA[⋯⋯]B[⋯⋯]=C[⋯⋯]A\begin{bmatrix} \cdots \\ \cdots \end{bmatri
2018-01-14 22:28:43
549
原创 Linear Algebra Lecture 2
Linear Algebra Lecture 21. Elimination2. Back-substitution3. Elimination matrices4. Multiply matricesExample 1 : To solve :⎧⎩⎨x+2y+z=23x+8y+z=124y+z=2\begin{cases}x+2y+z =2\\3x
2018-01-13 22:52:18
274
原创 Linear Algebra Lecture 1
Linear Algebra Lecture 11. n linear equations & n unknowns2. Row picture3. Column picture4. Matrix formThe fundamental problem of linear algebra which is to solve a system of linea
2018-01-12 23:13:32
362
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