Item:Q2146 - Revision history

Rongzhou: Updated the item for Definition: vector space hyperplane from Special:Update

2026-10-12T11:07:10Z

Updated the item for Definition: vector space hyperplane from Special:Update

← Older revision		Revision as of 11:07, 12 October 2026
Property / instance of
	~~mathematical expression~~
Property / instance of: mathematical expression / rank
	~~Normal rank~~
Property / LaTeX source
	~~P=\\left\\{ \\vec p + \\sum_{i=1}^{k} \\lambda_{i}\\vec v_{i}\\, \|\\, \\vec p,\\vec v_i \\in V,k < \\dim(V), \\lambda_{i} \\in \\mathbb{F} \\right\\} \\\\~~
Property / LaTeX source: P=\\left\\{ \\vec p + \\sum_{i=1}^{k} \\lambda_{i}\\vec v_{i}\\, \|\\, \\vec p,\\vec v_i \\in V,k < \\dim(V), \\lambda_{i} \\in \\mathbb{F} \\right\\} \\\\ / rank
	~~Normal rank~~
Property / note
	~~Then:\n\nP is a hyperplane of dimension $k$ in $V \\iff \\{\\vec v_i\\}$ is [[linearly independent#vectors\|linearly independent]]~~
Property / note: Then:\n\nP is a hyperplane of dimension $k$ in $V \\iff \\{\\vec v_i\\}$ is [[linearly independent#vectors\|linearly independent]] / rank
	~~Normal rank~~
Property / attributed to
	~~Rong Martin-Siebler ZHOU~~
Property / attributed to: Rong Martin-Siebler ZHOU / rank
	~~Normal rank~~
		Property / instance of
			mathematical expression
		Property / instance of: mathematical expression / rank
			Normal rank
		Property / LaTeX source
			P=\\left\\{ \\vec p + \\sum_{i=1}^{k} \\lambda_{i}\\vec v_{i}\\, \|\\, \\vec p,\\vec v_i \\in V,k < \\dim(V), \\lambda_{i} \\in \\mathbb{F} \\right\\}, \\\\
		Property / LaTeX source: P=\\left\\{ \\vec p + \\sum_{i=1}^{k} \\lambda_{i}\\vec v_{i}\\, \|\\, \\vec p,\\vec v_i \\in V,k < \\dim(V), \\lambda_{i} \\in \\mathbb{F} \\right\\}, \\\\ / rank
			Normal rank
		Property / note
			and $\\{\\vec v_i\\}$ is [[linearly independent#vectors\|linearly independent]],\n\nThen $P$ is a hyperplane of dimension $k$ in $V$
		Property / note: and $\\{\\vec v_i\\}$ is [[linearly independent#vectors\|linearly independent]],\n\nThen $P$ is a hyperplane of dimension $k$ in $V$ / rank
			Normal rank
		Property / attributed to
			Rong Martin-Siebler ZHOU
		Property / attributed to: Rong Martin-Siebler ZHOU / rank
			Normal rank

Rongzhou: Added content item: Definition: vector space hyperplane

2026-10-12T09:20:37Z

Added content item: Definition: vector space hyperplane

← Older revision		Revision as of 09:20, 12 October 2026
Property / instance of
	~~mathematical expression~~
Property / instance of: mathematical expression / rank
	~~Normal rank~~
Property / LaTeX source
	~~P=\\left\\{ \\vec p + \\sum_{i=1}^{k} \\lambda_{i}\\vec v_{i}\\, \|\\, \\vec p,\\vec v_i \\in V,k < \\dim(V), \\lambda_{i} \\in \\mathbb{F} \\right\\} \\\\~~
Property / LaTeX source: P=\\left\\{ \\vec p + \\sum_{i=1}^{k} \\lambda_{i}\\vec v_{i}\\, \|\\, \\vec p,\\vec v_i \\in V,k < \\dim(V), \\lambda_{i} \\in \\mathbb{F} \\right\\} \\\\ / rank
	~~Normal rank~~
Property / note
	~~Then:\n\nP is a hyperplane of dimension $k$ in $V \\iff \\{\\vec v_i\\}$ is [[linearly independent#vectors\|linearly independent]]~~
Property / note: Then:\n\nP is a hyperplane of dimension $k$ in $V \\iff \\{\\vec v_i\\}$ is [[linearly independent#vectors\|linearly independent]] / rank
	~~Normal rank~~
Property / attributed to
	~~Rong Martin-Siebler ZHOU~~
Property / attributed to: Rong Martin-Siebler ZHOU / rank
	~~Normal rank~~
		Property / instance of
			mathematical expression
		Property / instance of: mathematical expression / rank
			Normal rank
		Property / LaTeX source
			P=\\left\\{ \\vec p + \\sum_{i=1}^{k} \\lambda_{i}\\vec v_{i}\\, \|\\, \\vec p,\\vec v_i \\in V,k < \\dim(V), \\lambda_{i} \\in \\mathbb{F} \\right\\} \\\\
		Property / LaTeX source: P=\\left\\{ \\vec p + \\sum_{i=1}^{k} \\lambda_{i}\\vec v_{i}\\, \|\\, \\vec p,\\vec v_i \\in V,k < \\dim(V), \\lambda_{i} \\in \\mathbb{F} \\right\\} \\\\ / rank
			Normal rank
		Property / note
			Then:\n\nP is a hyperplane of dimension $k$ in $V \\iff \\{\\vec v_i\\}$ is [[linearly independent#vectors\|linearly independent]]
		Property / note: Then:\n\nP is a hyperplane of dimension $k$ in $V \\iff \\{\\vec v_i\\}$ is [[linearly independent#vectors\|linearly independent]] / rank
			Normal rank
		Property / attributed to
			Rong Martin-Siebler ZHOU
		Property / attributed to: Rong Martin-Siebler ZHOU / rank
			Normal rank

Rongzhou: Added content item: Definition: vector space hyperplane

2026-10-12T09:20:37Z

Added content item: Definition: vector space hyperplane

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