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it is the equivalent of the dot product of those vectors (i.e. dot(x, y)). d=a⃗⋅b⃗d=[a1a2a3a4]∗[b1b2b3b4] \begin{array}{c} d = \vec{a} \cdot \vec{b} \\ \end{array} \\ \begin{array}{c} d = \begin{bmatrix} a_1 & a_2 & a_3 & a_4\\ \end{b...
axb,xa1b(a0)AXB,X?Definition1LetAbeasquarematrixofordern,ifthereexistsasquarematrixBsuchthatABBAE,whereEistheidentitymatrixofordern,thenBiscalledtheinverseofA,andAissaidtobeinvertible.SupposeB,CarebothinversematricesofA,thatis,ABBAE,ACCAE thenBBEB(AC)(BA)CECC Thatis,theinverseofamatrix(ifitexists...
Consider a Householder matrix H1 defined as (2.73)H1=I−2uuT where I is the n× n identity matrix and u is a n× 1 unit vector which will be determined below. H1 is an orthogonal matrix such that H1T = H1− 1. We verify this below. (2.74)H1H1T=I−2uuTI−2uuTT=IT−...
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The Shank3 gene encodes the major postsynaptic scaffolding protein SHANK3. Its mutation causes a syndromic form of autism spectrum disorder (ASD): Phelan-McDermid Syndrome (PMDS). It is characterized by global developmental delay, intellectual disorders
Moreover, it has been reported that progression of a disease is the result of any dynamic change in structural components of ECM. The disease could be managed using such therapeutic molecules that help to control these changes of ECM environment. Many scientific reports have explained that ECM ...
2a). Importantly, this transformation is due to a growth component, described by the growth deformation tensor \({\Bbb{G}}\), and an elastic component, described by the elastic deformation gradient tensor \({\Bbb{A}}\) (such that \({\Bbb{F}}={\Bbb{A}}{\Bbb{G}}\)). Fig. 2:...
Matrigel, a mouse tumor extracellular matrix protein mixture, is an indispensable component of most organoid tissue culture. However, it has limited the utility of organoids for drug development and regenerative medicine due to its tumor-derived origin, batch-to-batch variation, high cost, and safe...
Our findings provide new evidence that the lens capsule is a unique and dynamic matrix structure closely linked to an extracapsular zone rich in connective tissue-like matrix proteins and has features integral to the different regions of the eye with which its matrix compartments interact. Results ...