UC知道数学毕业外文翻译,不需要翻译公式!!谢谢大家!!!
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The goal of this section is to state conditions under which a linear transformation can
be diagonalized. We shall be dealing with vector spaces over either the reals or the
complex numbers. We refer to the main theorems of this section as “principal axes
theorems” because they can be interpreted as asserting the existence of certain coordinate
systems (coordinate axes) with respect to which the transformation has a particularly
simple description. Such diagonalization theorems are special cases of what
are usually called “spectral theorems” in the literature because they deal with the
eigenvalues (the “spectrum”) of the transformation.
f ai i af
i
k
i i
i
k
v v
= =
  Ê
Ë Á
ˆ
¯ ˜
= ( )
0 0
.
f :sÆt
1.8 Principal Axes Theorems 37
v2
D2
D1 D0
v0 v1
w
Figure 1.18. Barycentric coordinates an
be diagonalized. We shall be dealing with vector spaces over either the reals or the
complex numbers. We refer to the main theorems of this section as “principal axes
theorems” because they can be interpreted as asserting the existence of certain coordinate
systems (coordinate axes) with respect to which the transformation has a particularly
simple description. Such diagonalization theorems are special cases of what
are usually called “spectral theorems” in the literature because they deal with the
eigenvalues (the “spectrum”) of the transformation.
f ai i af
i
k
i i
i
k
v v
= =
  Ê
Ë Á
ˆ
¯ ˜
= ( )
0 0
.
f :sÆt
1.8 Principal Axes Theorems 37
v2
D2
D1 D0
v0 v1
w
Figure 1.18. Barycentric coordinates an
目标，本节是国家在何种条件下可以转化为线性
被 。我们应处理向量空间超过要么雷亚尔或
复杂的数字。我们指的是主要定理本节为“主轴
定理“ ，因为它们可以被解释为主张存在某些协调
系统（坐标轴）这方面的转变有特别
简单的描述。这种对角化定理是什么特殊情况
通常所谓的“谱定理”的文学，因为他们处理
特征值（下称“频谱” ）的转变。
f爱字母i自动对焦
字母i
k
我我
字母i
k
v v
= =
a有é
权证
¯ 〜
= （ ）
0 0
。
传真： sÆt
1.8主轴定理37
2版
D2类
素D1 D0
v0 V1导联
瓦特
图1.18 。重心坐标和数量的比率。
归根结底，这将反过来，一个转变是如果
与此相关的矩阵是对称的或厄米特。不幸的是，这些性能
矩阵不是独立的基础上，被用来确定矩阵。为了
例如，有可能找到一个转型和两个基地，使矩阵
对称的一个方面，而不是对称的基础上对其他。那个
定义，抓住了本质上的对称性，我们需要的是，
“伴随”的转变。