In linear algebra, a defective matrix is a square matrix that does not have a complete basis of eigenvectors, and is therefore not diagonalizable. In particular, an n × n matrix is defective if and only if it does not have n linearly independent eigenvectors. A complete basis is formed by augmenting the eigenvectors with generalized eigenvectors, which are necessary for solving defective systems of ordinary differential equations and other problems.
An n × n defective matrix always has fewer than n distinct eigenvalues, since distinct eigenvalues always have linearly independent eigenvectors. In particular, a defective matrix has one or more eigenvalues λ with algebraic multiplicity m > 1 (that is, they are multiple roots of the characteristic polynomial), but fewer than m linearly independent eigenvectors associated with λ. If the algebraic multiplicity of λ exceeds its geometric multiplicity (that is, the number of linearly independent eigenvectors associated with λ), then λ is said to be a defective eigenvalue. However, every eigenvalue with algebraic multiplicity m always has m linearly independent generalized eigenvectors.
A Hermitian matrix (or the special case of a real symmetric matrix) or a unitary matrix is never defective; more generally, a normal matrix (which includes Hermitian and unitary as special cases) is never defective.
Minsan pag napahinga ng medyo matagal nagboboot pa. Pero madalas ganyan na. Nito lang yan nasira wala pang 1month.
Tingin ko overused saken 'to kaya nagkaganito. Nakahigh setting sa power setting palagi yan nung nagagamit kopa, tas ginagamit koren habang nakacharge.
Nagpalit naren ako thermal...
Hello,
Can anyone help me with my MacBook Pro 2017 running MacOS High Sierra?
Issue:
After updating, the MacBook froze and got stuck in a flashing question Mark folder. I was able to fix this by using the recovery tool, wiping out the SSD and reinstalling the macOS.
After reinstalling, I was...
A netizen has shared a cautionary tale about buying vehicles from Geely after his two-year-old car became worse for wear following a repair attempt by the Chinese automotive maker.
James Afante posted a Tiktok video demanding proper repair of his barely 2-year-old Coolray unit.
Full article...
Meron kasi akong nabili na "80+ bronze psu" - AITC Kingsman KN650 (taiwan brand), kailangan ko kasi agad ng replacement psu at out of stock yung known brand na psu dun sa shop na pinuntahan ko.
Ang issue nagsimula mga 3 days pagkatapos kong bilhin itong psu. Kapag bagong bukas kasi - yung first...
For sale as Defective RX 570 8GB nagamit lang sa Roblox
2,500 paayos sabi nung gpu level technician ewan ko lang sa iba kung mas mahal o mas mura
issue: No display No fan Spinning
bigla nag no display habang nag iinstall ng Windows 10
okay pa naman physically no damage corrotion or sunog...
Goodevening
Possible po ba na glass replacement lang ang gawin sa S6 Edge? Or possible din po ba yung defective na S6 Edge pero working ang lcd at ilipat ang mga components dun?
Nabububog na po ako sa screen ko hehehe
Thankyou in advance
Goodevening po
May mga thoughts po ba kayo about sa pagswap ng parts sa cellphone? Pa advice naman po, plano ko po gamitin yung defective ko na s6 edge para sa LCD pamalit dito sa ngayon ko, at sa tingin niyo po ba pwede ko ipakabit to sa technician?
Thankyou in advance