Polyphonic Music Represented in Mathematical Vectors
... are 6 notes. Other voices are filled with notes of the same pitch to get the same number of notes within a bar. Number of notes in bar 1 is set to 6 for each voice. Therefore harmonic matrix H1 consists of 6 chords (columns). Next harmonic matrix H2 will have just 2 chords, since max number of note ...
... are 6 notes. Other voices are filled with notes of the same pitch to get the same number of notes within a bar. Number of notes in bar 1 is set to 6 for each voice. Therefore harmonic matrix H1 consists of 6 chords (columns). Next harmonic matrix H2 will have just 2 chords, since max number of note ...
Nonsymmetric algebraic Riccati equations and Wiener
... To get a nice theory for the equation (1.2), we need to add some conditions on the matrices A, B, C, and D, much the same as done for the symmetric equation (1.1). For any matrices A, B ∈ Rm×n , we write A ≥ B(A > B) if aij ≥ bij (aij > bij ) for all i, j. We can then define positive matrices, nonne ...
... To get a nice theory for the equation (1.2), we need to add some conditions on the matrices A, B, C, and D, much the same as done for the symmetric equation (1.1). For any matrices A, B ∈ Rm×n , we write A ≥ B(A > B) if aij ≥ bij (aij > bij ) for all i, j. We can then define positive matrices, nonne ...
