Last Updated
：2025/12/04
rank-nullity theorem
Noun
uncountable
Japanese Meaning
ある線形変換または対応する行列に関する定理で、変換の階数（rank）と零空間の次元（nullity）の和が、その変換の定義域である全ベクトル空間の次元に一致することを示す定理。
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(linear algebra) A theorem about linear transformations (or the matrices that represent them) stating that the rank plus the nullity equals the dimension of the entire vector space (which is the linear transformation’s domain).
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rank-nullity theorem
When solving systems of linear equations, understanding the rank-nullity theorem helps determine whether solutions exist and how many degrees of freedom they have.
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When solving systems of linear equations, understanding the rank-nullity theorem helps determine whether solutions exist and how many degrees of freedom they have.
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