Proof that $\exp(ikx)$ forms an orthogonal basis of $L^2[-\pi,\pi]$
12698
Orthonormal basis for $\mathcal{L}^2([0,1])$
158156
Finding the dual basis for the space of polynomials of degree $\leq$ 2
27086
proof for $\langle q| p \rangle = e^{ipq}$
152932
Proof: $\det\pmatrix{\langle v_i , v_j \rangle}\neq0$ $\iff \{v_1,\dots,v_n\}~\text{l.i.}$
153589
Integral basis of an extension of number fields
32606
Is the operator $T((x_1,x_2,...,x_n))=(x_1,\frac{x_2}2,\frac{x_3}3,...)$ on $\ell^2$ self-adjoint and unitary
119352
compact and self adjoint square root of an operator
29230
Orthogonality of Hermite functions
138342
Proof of a matrix exponential identity
26968
Proof that the series expansion for exp(1) is a Cauchy sequence
127000
When does $V = \ker(f) \oplus \operatorname{im}(f)$?
14550
Every Hilbert space has an orthonomal basis - using Zorn's Lemma
132411
Fourier series coefficients proof
144531
How to prove that a nilpotent operator has a basis representation that is strictly upper triangular?
143765
To Show that $\exp(tX)\exp(tY)= \exp(t(X+Y)) + (1/2)t^2[X, Y] +o(t^3)$
146839
Orthogonal Projection onto the $ {L}_{\infty} $ Unit Ball
58741
Operator Exponential $e^A e^B = e^{A+B}$