in an infinite dimensional space there always exist two subspaces whose vector sum is different from their span . 在一無限空間中恒存在兩個子空間,其矢量和與其張成空間不同。
by translations and changes of scale the spectral subspaces associated with all discs can be characterized similarly . 通過平移與尺度改變,伴隨著一切圓域的譜子空間都可以類似地給予刻劃。
one of the most important, most difficult, and most exasperating unsolved problems of operator theory is the problem of invariant subspaces . 算子理論中最重要、最困難也最令人煩惱的未解決問題之一就是不變子空間問題。
the cheapest way to get one is to invoke the spectral theorem and to conclude that normal operators always have non-trivial invariant subspaces . 取得這樣結(jié)果的最省力的嘗試是引用光譜定理而得到正規(guī)算子恒有非平凡不變子空間的結(jié)論。
a digital watermarking algorithm based on subspace 基于分形壓縮編碼的數(shù)字水印技術(shù)