Indices Homework Help: 4x4 = 16 Equations?

schwarzschild · 2010-04-11T23:17:50+00:00

I'm not sure I understand how: T^{\alpha \mu \lambda}A_{\mu}C_{\lambda}^{\gamma} = D^{\gamma \alpha} "Represents 16 different equations..." My thinking was that \alpha and \gamma each have four possible values \left\{0,...3 \right\} so we have 4 \cdot 4 = 16 different equations - is that correct?

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Thread starter schwarzschild
Start date Apr 11, 2010
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The discussion centers on the equation T^{\alpha \mu \lambda}A_{\mu}C_{\lambda}^{\gamma} = D^{\gamma \alpha}, which represents 16 distinct equations. Participants confirm that since both indices α and γ can each take on four values (0 to 3), the total number of combinations is indeed 4 multiplied by 4, resulting in 16 equations. This understanding is crucial for grasping the implications of tensor notation in mathematical physics.

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Apr 11, 2010

schwarzschild

I'm not sure I understand how:

[tex]T^{\alpha \mu \lambda}A_{\mu}C_{\lambda}^{\gamma} = D^{\gamma \alpha}[/tex]

"Represents 16 different equations..."

My thinking was that [tex]\alpha[/tex] and [tex]\gamma[/tex] each have four possible values [tex]\left\{0,...3 \right\}[/tex] so we have [tex]4 \cdot 4 = 16[/tex] different equations - is that correct?