"ούτω γάρ ειδέναι το σύνθετον υπολαμβάνομεν, όταν ειδώμεν εκ τίνων και πόσων εστίν …"

21 Sep

In exercise [1, p. 34 exercise 2.2] we are asked to
prove that the rows and columns of a unitary matrix are orthonormal as per [1, p. 21,(2.21)].
read the conclusion >

21 Sep

In exercise [1, p. 34 exercise 2.1] we are asked to prove that the inverse of a lower triangular matrix is also lower triangular by using relation [1, p. 23, (2.30)].
read the conclusion >

13 Jun

In exercise [1, p. 34 exercise 2.5] we are asked to show that
the matrix is circulant
when .
read the conclusion >

1 Feb

The exercise [1, p. 34 exercise 2.4] asks to show that if is a full rank matrix with > , is a vector, and is an vector, that the effect of the linear transformation

is to project onto the subspace spanned by the columns of . Specifically, if are the columns of , the exercise [1, p. 34 exercise 2.4] asks to show that

Furthermore it is asked why the transform must be idempotent. read the conclusion >

(1) |

is to project onto the subspace spanned by the columns of . Specifically, if are the columns of , the exercise [1, p. 34 exercise 2.4] asks to show that

(2) |

Furthermore it is asked why the transform must be idempotent. read the conclusion >

2 Jan

Exercise [1, p. 14 exercise 1.1] asks to prove that

is a monotonically increasing function over the interval . Furthermore it asks to show that due to the monotonicity of the peaks of the spectral estimate shown in [1, Figure 1.2b] that they must also be present in the spectral estimate of [1, Figure 1.2a]. read the conclusion >

(1) |

is a monotonically increasing function over the interval . Furthermore it asks to show that due to the monotonicity of the peaks of the spectral estimate shown in [1, Figure 1.2b] that they must also be present in the spectral estimate of [1, Figure 1.2a]. read the conclusion >