Inner product space
84 videos • 10,579 views • by billionaire icon
1
Schwarz Inequality in Inner Product Space, BSc and MSc maths
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2
Every inner product space is a norm linear space , inner product space msc maths
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3
jointly continuous property of inner product space , msc maths
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4
parallelogram law in inner product space for bsc and msc maths
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5
polarisation identity in inner product space for msc and bsc maths
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6
Apollinias identity in inner product space, msc mathematics
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7
Every Cauchy sequence is bounded in an inner product space, msc mathematics
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8
inner product of two cauchy sequence is cauchy and convergent , inner product space msc maths
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9
A real norm linear space which holds parallelogram law is an inner product space , IPS
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10
Definition of Hilbert Space with example, Inner Product Space
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11
Example of an Inner Product Space which is not Hilbert Space, Inner Product Space
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12
Example of a space which is not a Hilbert Space, Inner Product Space , MSc mathematics
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13
L[0,1] with respect to given norm does not satisfy parallelogram law, Inner Product Space ,Msc math
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14
Convex Set and its properties, Inner Product Space, MSc mathematics
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15
Closed, convex subpace of hilbert space contains a unique vector of smallest norm , IPS
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16
closed subspace M of Hilbert space contains unique vector such that ||x- y||=d , y is vector in M
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17
Definition of orthogonal set with its properties, Inner Product Space
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18
Pythagorian theorem, Inner Product Space, MSc Mathematics
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19
Proper closed subspace of H , is orthogonal to non zero vector of H, Inner product space
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20
Orthogonal Complement of a set in Inner Product Space, MSc Mathematics
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21
Properties of Orthogonal Complement for non empty subsets of Hilbert Space H, IPS
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22
Bessel's Inequality for finite orthonormal set, Inner Product Space
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23
Self Adjoint Operator in Hilbert Space with example, Inner Product Space
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24
Self Adjoint Operators set form a non-empty real banach space , Inner Product Space
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25
Product of two self adjoint operator is self adjoint iff they commute & T=0 iff (Tx, y)=0 ,IPS
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26
If T is an operator on H then T = 0 iff (Tx, x) = 0 for all x in H, Inner Product Space
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27
An Operator T is self adjoint iff (Tx, x) is real for all x in H, Inner Product Space
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28
Positive Operator with example, hilbert space, Inner Product Space
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29
TT* and T*T are positive operators on hilbert space H, Inner Product Space
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30
Unique representation of T in terms of two self adjoint operators on H, Inner Product Space
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31
If A positive operator on H then I + A is non singular on H, Inner Product Space
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32
Normal Operator Definition with examples, Inner Product Space
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33
Every Normal Operator need not be self adjoint operator, Inner Product Space
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34
(αT + βT*) is normal operator where T is arbitrary and |α| = |β|, Inner Product Space
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35
property of normal operator, Inner Product Space
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36
N(H) closed subset of B(H), contains self adjoint operators , closed under scalar multiplication
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37
Operator T on H is normal iff ||Tx|| = ||T*x||
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38
If N is normal operator then ||N^2|| = ||N||^2 , Inner Product Space
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39
If N is normal operator then ||N^2|| = ||N||^2 , Inner Product Space
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40
Definition of Unitary operator with examples, Inner Product Space
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41
Necessary and sufficient condition for an operator to be unitary operator, Inner Product Space
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42
example of a linear isometry on H which is not unitary operator, Inner Product Space
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43
some equivalent statements for an operator T on hilbert space H, Inner Product Space
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44
Definition of Projection on Banach space
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45
P is projection on H, M orthogonal to N iff P is self adjoint and N = M orthogonal
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46
Definition of Projection on hilbert space...
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47
P projection on M then I - P projection on M orthogonal
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48
Some important properties of projection on hilbert space H
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49
Gram Schmidth Orthogonalisation Process, Inner Product Space |by Sapna|
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50
Parseval's Identity, Inner Product Space | by Sapna |
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51
To show that fy is functional from Hilbert space H to C (Complex), Inner Product Space | by Sapna |
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52
Riesz Representation Theorem, Inner Product Space | by Sapna |
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53
H hilbert space then H* also holbert space, Inner Product Space | by Sapna |
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54
one-one, onto, additive, isometry but not linear property of a map, Inner Product Space
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55
Definition of Conjugate of an Operator, Inner Product Space | by Sapna |
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56
Operator T continuous , there exists unique adjoint operator T* which is LT and continuous, IPS
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57
T non singular then T* also non singular | by Sapna |
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58
Properties of Adjoint Operation , Inner Product Space | by Sapna | @billionaireicon3311
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59
Properties of Projection on Closed linear subspace M of H , Inner Product Space | by Sapna |
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60
Definition of Invariant under T and M reduces T , Inner Product Space | by Sapna |
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61
M invariant under T iff M orthogonal invariant under T* , Inner Product Space | by Sapna |
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62
M reduces T iff M is invariant under T and T* , Inner Product Space | by Sapna |
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63
M is invariant under T iff TP = PTP, Inner Product Space | by Sapna |
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64
M reduces T iff TP = PT, Inner Product Space | by Sapna | @billionaireicon3311
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65
Definition of Projection Orthogonality , Inner Product Space | by Sapna | @billionaireicon3311
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66
Sum of Pi's are projection iff Pi's are pairwise orthogonal , | by Sapna | @billionaireicon3311
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67
PQ projection iff PQ=QP and Range will be intersection of both range spaces, Inner Product Space
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68
Some equivalent statements on Projections , Inner Product Space @billionaireicon3311
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69
Difference Q - P is projection iff P≤Q , Inner Product Space | by Sapna | @billionaireicon3311
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70
An idempotent operator on hilbert space H is projection iff it is normal @billionaireicon3311
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71
Proper Eigen Vector, Value, Eigen Space , Inner Product Space | by Sapna | @billionaireicon3311
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72
Eigen Space invariant under T and closed linear subspace of H | by Sapna | @billionaireicon3311
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73
If T normal operator then each Eigen spaces reduces T | by Sapna | @billionaireicon3311
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74
Some equivalent statements under Finite Dimensional Spectral Theory | by Sapna |
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75
Hilbert space finite dim iff every complete orthonormal set is basis for H | by Sapna |
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76
Some definitions under Measure space, Measure Theory | by Sapna | @billionaireicon3311
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77
Definition of measure mu , Measure Space | by Sapna | @billionaireicon3311
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78
Signed Measure nu , Measure Space | by Sapna | @billionaireicon3311
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79
Definition of a positive set and result based on that , Measure Space | by Sapna |
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80
Definition of negative set and result based on that, Measure Space | by Sapna |
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81
Null set and a result based on that , Measure Space | by Sapna | @billionaireicon3311
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82
Hahn Decomposition, Measure Theory | by Sapna | @billionaireicon3311
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83
Hahn Decomposition Theorem, Measure Theory | by Sapna | @billionaireicon3311
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84
Mutually Singular Measure , Positive and Negative Variation , Measure Theory @billionaireicon3311
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