This paper investigates the capacity of multi-antenna Gaussian channels in a point-to-point communication system. The authors consider a system with \( t \) transmit antennas and \( r \) receive antennas, where the received vector \(\mathbf{v}\) depends on the transmitted vector \(\mathbf{u}\) through the channel matrix \( H \) and additive Gaussian noise \(\mathbf{w}\). The channel capacity is given by a formula involving the eigenvalues of \( H \). The first part of the paper focuses on maximizing the capacity by optimizing the eigenvalues \(\lambda_i\) and power allocations \( P_i \) under constraints on total power and the sum of eigenvalues. For line-of-sight channels, the optimal solution depends on the signal-to-noise ratio (SNR). At low SNR, a single strong channel is optimal, while at high SNR, multiple parallel channels are optimal. The second part of the paper examines the pessimistic capacity, where the eigenvalues are chosen by an adversary to minimize the channel capacity. Two scenarios are considered: when the eigenvalues are known only at the receiver and when they are known at both ends. In the first scenario, a uniform power distribution and a single non-zero eigenvalue are optimal. In the second scenario, all eigenvalues must be non-zero, and the minimum capacity is achieved when all eigenvalues are equal, except for one dominant eigenvalue. The threshold for this scenario is \( T > 4(n-1) \). The paper provides insights into the trade-offs between joint optimization and worst-case analysis in multi-antenna systems.This paper investigates the capacity of multi-antenna Gaussian channels in a point-to-point communication system. The authors consider a system with \( t \) transmit antennas and \( r \) receive antennas, where the received vector \(\mathbf{v}\) depends on the transmitted vector \(\mathbf{u}\) through the channel matrix \( H \) and additive Gaussian noise \(\mathbf{w}\). The channel capacity is given by a formula involving the eigenvalues of \( H \). The first part of the paper focuses on maximizing the capacity by optimizing the eigenvalues \(\lambda_i\) and power allocations \( P_i \) under constraints on total power and the sum of eigenvalues. For line-of-sight channels, the optimal solution depends on the signal-to-noise ratio (SNR). At low SNR, a single strong channel is optimal, while at high SNR, multiple parallel channels are optimal. The second part of the paper examines the pessimistic capacity, where the eigenvalues are chosen by an adversary to minimize the channel capacity. Two scenarios are considered: when the eigenvalues are known only at the receiver and when they are known at both ends. In the first scenario, a uniform power distribution and a single non-zero eigenvalue are optimal. In the second scenario, all eigenvalues must be non-zero, and the minimum capacity is achieved when all eigenvalues are equal, except for one dominant eigenvalue. The threshold for this scenario is \( T > 4(n-1) \). The paper provides insights into the trade-offs between joint optimization and worst-case analysis in multi-antenna systems.