linear algebra 08/17/2017 lecture 11

symmetric & upper triangular matrix = diagonal matrix.  dimension = 3  in 3*3 matrix

Sum: symmetric or upper triangular matrix : take anything in S and anything in U. 不是并集，是相加。 所以可以得到all matrix. dimension (S+U) = 9 in 3*3 matrix

dim(S) +dim(U) = dim(S&U) + dim(S+U)

rank 1 matrix
example : A is 2*3 matrix

rank 1 matrix 像积木，eg. 一个rank 4 的matrix可以分解成4个rank 1 matrix的相乘

subset of rank 1 matrix can't form a sub space (两个rank 1 matrix相加可能得到一个rank 2 matrix)

In R4, V = [v1,v2,v3,v4], S is all v in R4 to make v1+v2+v3+v4 = 0
=>Av = 0 A = [1,1,1,1]
S 是A的null space. RA = 1 => S = R(N(A)) = n-r = 4-1 = 3
三个特殊解找出来即可

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