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特征值与特征向量

数学上,线性变换特征向量(本征向量)是一个非退化向量,其方向在该变换下不变。该向量在此变换下缩放的比例称为其特征值(本征值)。 图1给出了一幅图像的例子。一个变换通常可以由其特征值和特征向量完全描述。特征空间是相同特征值的特征向量的集合。这些概念在纯数学应用数学的很多领域发挥着巨大的作用—在线性代数泛函分析,甚至在一些非线性的情况中也有着显著的重要性。「特征」一詞來自德语的eigen。1904年希耳伯特首先在这个意义下使用了这个词,更早亥姆霍兹也在相关意义下使用过该词。eigen一詞可翻译为“自身的”,“特定于...的”,“有特征的”或者“个体的”—这强调了特征值对于定义特定的变换有多重要。

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(Oryza)是草本稻屬植物的統稱。為一年生,禾本科植物,单子叶,性喜温湿,成熟時約有1到1.8米高,葉子細長,約有50到100公分長,寬約2到2.5公分。稻米的花非常小,開花時,主要花枝會呈現拱形,在枝頭往下30到50公分間都會開小花,大部分自花授粉並結種子,稱為稻穗。一般稻穗的大小在5到12毫米長,2到3毫米厚度。稻是人類重要的糧食作物之一,耕種與食用的歷史都相當悠久。全世界有一半的人口食用它。主要在亚洲欧洲南部和热带美洲非洲部分地区。总产量占世界粮食作物产量第三位,低于玉米小麦,但能维持较多人口的生活,所以联合国2004年定为“国际稻米年”。

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梳士巴利道
梳士巴利道(Salisbury Road,舊稱疏利士巴利道),位於香港九龍尖沙咀海旁,是香港著名道路之一。道路西端位於尖沙咀天星碼頭一帶連接廣東道,然後沿著尖沙咀海濱公園,東面連接紅磡繞道。梳士巴利道於1900年代隨著九廣鐵路尖沙咀段於海旁填海時一併建成,並以當時英國首相Salisbury (索爾茲伯里侯爵)命名。值得留意的是,當時的中文譯名按英文字母串法,稱作疏利士巴利道。然而,Salisburyi是不發音的。所以香港政府1970年代將該路的中文名稱改作現今名稱。

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