Linear algebra || Subspace || Def & Examples , theorems || lecture 3 ||

Main module wise topics:-

Linearalgebra, vectorspaces, lineartransformation, matrices, diagonalizability, canonicalforms, innerproductspace, bilinearform, quadraticform,

Sub topics :-
Vectorspace, subspace, linearcombination, linearspan, LI, LD, basis, dimension, directsum, quotientspace, firstisomorphismtheorem, secondisomorphismtheorem,
Thirdisomorphismtheorem,
Counting,

lineartransformations, Range, rank, nullity, nullspace, sylvesterlaw, compostionmap, projection, orthogonalprojection, reflection, rotation,

Matrixrepresentation, eigenvalue, eigenvector, charactertisticpolynomial, cayleyhamiltontheorem, monicpolynomial, minimalpolynomial, companionmatrix, eigenspace, geometricmultiplicity, algebraicmultiplicity, GM, AM, gersgorintheorem, similiarity,

Diagonalization, specturm, permutationmatrix, Jordancanonicalforms,

Innerproductspace, gramschmidtorthogonalprocess, isomorphism, unitary, normal, spectraltheorem, cauchyschwarzinequality,

Bilinearform, quadraticform, annihilator, definite, semidefinite, indefinite, hadamardinequality, congruenceofmatrix, signatureandindex,

#Linearalgebra, #vectorspaces, #lineartransformation, #matrices, #diagonalizability, #canonicalforms, #innerproductspace, #bilinearform, #quadraticform,

#Vectorspace, #subspace, #linearcombination, #linearspan, #LI, #LD, #basis, #dimension, #directsum, #quotientspace, #firstisomorphismtheorem, #secondisomorphismtheorem,
#Thirdisomorphismtheorem,
#Counting,