线性代数复习分析(矩阵代数运算)
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分类题部分
2.3 数字矩阵求逆
1.有关伴随矩阵求逆部分的处理
时刻记住最后要进行一布倒置的步骤
如果有洞的话,请考虑用分块矩阵来处理
例如
then let it be the
then we can use the part to get the result
2.also use the row operation to help with it
assume that invertible matrix to be the A
then we can use the matrix
to use row operation and get what we want
then get the
2.4抽象矩阵代数运算
some judgement , then use some example
like
or
2。symmetric matrix’s judgement
use the
also it can apply to the complicated expression
such as
a very interesting question
assume that
prove that the matrix A ab A - 2E are invertible and help get their inverse matrix
prove
according to the question we can get that
so we can see that
so we can know that the det(A) is not equal to the 0 so the A is invertible
also we can prove that the matrix A-2E is invertible in the same way
the Reductio ad absurdum
description:assume that A is n*n matrix , and we have
that
and that
then please prove that the matrix A + E is not invertible
prove
please prove that
and use that
expansion the selected problem set
description
for every n*1 matrix X we have the
A = B
the method
then we denote the I as the (e1,e2,…..en) , then we can konw that every ej is a column vector then Aei = 0 is adequate for every i
then we can know that
then we can judge that
description:assume that A is a n*n matrix , and their exist a integer m , that can let the Am = 0 , and we know that B is a invertible matrix , try to prove that the equation
method
then assume that their exists a X != 0 and we can know that
and according to the question we can know that their exists a k > 0
that enable that
then
we can
附件
(阶梯形方程组),(方程组的初等变换),行阶梯矩阵(row echelon matrix),主元,简化行阶梯矩阵(reduced row echelon matrix),(高斯消元法(Gauss elimination)),(解向量),(同解),(自反性(reflexivity)),(对称性(symmetry)),(传递性(transitivity)),(等价关系(equivalence));(主变量),(自由位置量),(一般解),(齐次线性方程组的秩(rank));向量组线性相关,向量组线性无关,线性组合,线性表示,线性组合的系数,(向量组的延伸组);线性子空间,由向量组张成的线性子空间;基,坐标,(自然基),线性子空间的维数(dimension),向量组的秩;(解空间),齐次线性方程组的基础解系(fundamental system of solutions);(导出组),线性流形,(方向子空间),(线性流形的维数),(方程组的特解);(方程组的零点),(方程组的图象),(平面的一般方程),(平面的三点式方程),(平面的截距式方程),(平面的参数方程),(参数),(方向向量);(直线的方向向量),(直线的参数方程),(直线的标准方程),(直线的方向系数),(直线的两点式方程),(直线的一般方程);(平面束(pencil of planes)) 矩阵的秩与矩阵的运算 线性表示,线性等价,极大线性无关组;(行空间,列空间),行秩(row rank),列秩(column rank),秩,满秩矩阵,行满秩矩阵,列满秩矩阵;线性映射(linear mapping线性变换(linear transformation),线性函数(linear function);(零映射),(负映射),(矩阵的和),(负矩阵),(线性映射的标量乘积),(矩阵的标量乘积),(矩阵的乘积),(零因子),(标量矩阵(scalar matrix)),(矩阵的多项式);(退化的(degenerate)方阵),(非退化的(non-degenerate)方阵),(退化的线性变换),(非退化的线性变换),(逆矩阵(inverse matrix)),(可逆的(invertible),(伴随矩阵(adjoint matrix));(分块矩阵(block matrix)),(分块对角矩阵(block diagonal matrix));初等等矩阵(elementary matrix),等价(equivalent);(象空间),(核空间(kernel))(线性映射的秩),(零化度(nullity))
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