Definition: A symmetric matrix A is idempotent if A2=AA=A. A matrix A is idempotent if and only if all its eigenvalues are 0 or 1. Tus naj npawb ntawm eigenvalues sib npaug li 1 yog ces tr(A).
Yuav ua li cas koj thiaj paub yog matrix yog idempotent?
Idempotent matrix: Ib lub matrix tau hais tias yog idempotent matrix if matrix multiplied los ntawm nws tus kheej rov qab tib lub matrix. Lub matrix M yog hais tias yog idempotent matrix yog thiab tsuas yog MM=M. Nyob rau hauv idempotent matrix M yog ib tug square matrix.
Dab tsi ua rau matrix tsis muaj zog?
Tsuas yog cov lus tsis zoo ib yam idempotent matrix yog tus lej matrix; uas yog, yog hais tias ib tug tsis yog tus kheej matrix yog idempotent, nws tus naj npawb ntawm cov kab ywj siab (thiab kab) tsawg dua nws cov kab (thiab kab)., vim A yog idempotent.
Thaum lub matrix hu ua idempotent matrix?
Definition 1. Ib n × n matrix B hu ua idempotent if B2=B. Piv txwv Tus lej matrix yog idempotent, vim I2=I · I=I.
Yuav ua li cas rau lub square matrix ua idempotent?
Ib tug idempotent matrix yog ib tug square matrix uas thaum muab faib los ntawm nws tus kheej, muab lub resultant matrix li nws tus kheej. Hauv lwm lo lus, matrix P yog hu ua idempotent yog P2=P.
